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* &size(30){kenichiro のホ〖ムペ〖ジへようこそ}; [#b8a4f17c]

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//* &color(red,yellow){7/6-13 は叫磨のため稍哼です}; [#z06dae5b]
//&color(矢机咖,秦肥咖){インライン妥燎};
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//RIGHT:&size(15){[[眶池联饯ˇ眶池兜伴漓饯池栏脱息晚ペ〖ジへ:http://math.edu.ibaraki.ac.jp/index.php?id=9]] &br; [[∈榜倦络池兜伴池婶眶池兜伴兜技∷:http://math.edu.ibaraki.ac.jp/]]};

&size(15){沁 呐 夫办虾∈UMEZU Kenichiro∷}; &br;

//榜倦络池兜伴池婶眶池兜伴兜技 兜鉴 &br;

榜倦络池池窖甫垫薄 答撩极脸彩池填 &nbsp;兜鉴 &br;
[[兜伴池婶:http://www.edu.ibaraki.ac.jp/]]ˇ[[络池薄兜伴池甫垫彩:http://www.ppedu.ibaraki.ac.jp/]] 么碰

-[[researchmap:https://researchmap.jp/read0051534?lang=ja]]
-[[彩池甫垫锐锦喇祸度デ〖タベ〖ス:https://nrid.nii.ac.jp/ja/nrid/1000000295453/]] 
-[[榜倦络池甫垫荚攫鼠另枉:https://researchers.ibaraki.ac.jp/search/detail.html?systemId=69387a7ff286d6b7&lang=ja&st=fields]]

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''Email:'' &nbsp; &ref(emailaddr.png,nolink,95%); &br;

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''交疥¨'' ⅸ310-8512 榜倦俯垮竿辉矢叠2-1-1 榜倦络池兜伴池婶 &br;

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''甫垫技¨'' 兜伴池婶 D 棚 D307 &br;

[[榜倦络池垮竿キャンパスマップ:http://www.ibaraki.ac.jp/generalinfo/campus/mito/index.html]] &br;

//''Email:'' &nbsp; &ref(emailaddr.png,nolink,95%); &br;
//E-mail: &ref(150s_email.jpg);

//[[兜伴池婶眶池兜伴兜技のHP:http://math.edu.ibaraki.ac.jp/]]

//[[榜倦络池垮竿キャンパス:http://www.ibaraki.ac.jp/generalinfo/campus/mito/index.html]]
//′兜伴池婶′D棚′3超′307规技
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* 漓嚏尸填 [#c0d0bf5c]
- 眶池 > 豺老池 > 眶妄豺老池簇息 > 取眶数镍及侠·润俐妨豺老 > 润俐妨市腮尸数镍及侠 > 润俐妨率边房董肠猛啼玛
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* キ〖ワ〖ド [#x2917c95]
- 润俐妨率边房市腮尸数镍及
- 赖猛豺
- ロジスティック数镍及
- sublinear, concave-convex 润俐妨拉
- 润俐妨董肠掘凤
- 敛夺弄豺の妨觉
- 渡疥弄第び络拌弄尸呆妄侠
- Nehari manifold, 恃尸恕
- 疤陵弄缄恕
- 孺秤付妄·sub- and supersolutions
- 客庚瓢轮侠
//- 改挛眶泰刨
//- sublinear
//- concave-convex

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* 糠缅 [#c2805c09]

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//
// &nbsp; --- 染逞スペ〖ス

//----------------------------------------
// What's new ! 
//----------------------------------------

// スペ〖ス &nbsp; 染逞 &emsp; 链逞

- 2025-06-24 &br;
K. Umezu, Boundary layer profiles of positive solutions for logistic equation with sublinear nonlinearity on the boundary, submitted. [[arXiv:2506.19237:https://arxiv.org/abs/2506.19237]]  
//
- 2024-12-31 &br;
K.Umezu, Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case, 
'''Zeitschrift f&#252;r angewandte Mathematik und Physik''', ''76'', (2025), Article: 
25. [[10.1007/s00033-024-02409-2:https://doi.org/10.1007/s00033-024-02409-2]] &nbsp; [[Shared Link:https://rdcu.be/d5ibQ]] (view-only version) &nbsp; 
[[arXiv:2404.04574:http://arxiv.org/abs/2404.04574]] (downloadable) 
//
//- 2024-12-05 &br;
//K.Umezu, Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case, 
//[['''Zeitschrift f&#252;r angewandte Mathematik und Physik //(ZAMP)''':https://link.springer.com/journal/33]], (2024), accepted. 
//&nbsp; [[arXiv:2404.04574:http://arxiv.org/abs/2404.04574]] 
//

//- 2024-04-09 &br;
//K.Umezu, Diffusive logistic equation with a non Lipschitz nonlinear boundary condition arising from coastal fishery harvesting: the resonant case, (2024). //&nbsp; [[arXiv:2404.04574:http://arxiv.org/abs/2404.04574]] 
//
//- 2024-01-25 &br;
//K.Umezu, Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II, '''Journal of Mathematical Analysis and Applications''', ''534''(1), (2024), No.128134. 
//[[10.1016/j.jmaa.2024.128134:https://doi.org/10.1016/j.jmaa.2024.128134]]
//&nbsp;  ''Share Link(50 days' free access)''
//https://authors.elsevier.com/a/1iUFi,WNxuZyi

//[[arXiv.2301.12147:https://arxiv.org/abs/2301.12147]]

//- 2024-01-18 &br;
//K.Umezu, Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II, [['''Journal of Mathematical Analysis and Applications''':https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications]], in press. 
//[[arXiv.2301.12147:https://arxiv.org/abs/2301.12147]]

//- 2023-06-23 &br;
//Juli&#225;n L&#243;pez-G&#243;mez 黎栏 (Complutense University of Madrid, Spain)  が7奉13泣に[[榜倦络池垛退セミナ〖:http://enakai.sci.ibaraki.ac.jp/frisemi/]]で怪遍されますˉ

//- 2023-01-28 &br;
//K.Umezu, Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting II, preprint. 
//[[arXiv.2301.12147:https://arxiv.org/abs/2301.12147]]

//- 2023-01-04 &br;
//K.Umezu, Uniqueness of a positive solution for the Laplace equation with indefinite superlinear boundary condition, '''Journal of Differential Equations''', ''350'', (2023), 124-151. [[10.1016/j.jde.2022.12.017:https://doi.org/10.1016/j.jde.2022.12.017]]

//[[''Share Link'':https://authors.elsevier.com/a/1gMXn50j-rpdi]]
//[[arXiv:2107.07719:https://arxiv.org/abs/2107.07719]]

//- 2022-12-25 &br;
//K.Umezu, Uniqueness of a positive solution for the Laplace equation with indefinite superlinear boundary condition, [['''Journal of Differential Equations''':https://www.sciencedirect.com/journal/journal-of-differential-equations]], in press. 
//[[arXiv:2107.07719:https://arxiv.org/abs/2107.07719]]

//- 2022-12-19 &br;
//K.Umezu, Uniqueness of a positive solution for the Laplace equation with indefinite superlinear boundary condition, [['''Journal of Differential Equations''':https://www.sciencedirect.com/journal/journal-of-differential-equations]], accepted. 
//[[arXiv:2107.07719:https://arxiv.org/abs/2107.07719]]

//- 2022-11-09 &br;
//K.Umezu, Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting, '''Nonlinear Analysis: Real World Applications''', ''70'', (2023), Paper No.103788.  
//[[10.1016/j.nonrwa.2022.103788:https://doi.org/10.1016/j.nonrwa.2022.103788]]
//[[&color(red){Share Link};:https://authors.elsevier.com/a/1g2ps5Dp%7E-h-er]]
//[[arXiv:2202.09442:https://arxiv.org/abs/2202.09442]]

//- 2022-11-02 &br;
//K.Umezu, Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting, '''[[Nonlinear Analysis: Real World Applications:https://www.sciencedirect.com/journal/nonlinear-analysis-real-world-applications]]''', in press. 
//[[arXiv:2202.09442:https://arxiv.org/abs/2202.09442]]

//- 2022-05-21 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results. '''Israel Journal of Mathematics''', ''247'', (2022), 661-696.  [[10.1007/s11856-021-2278-y:https://doi.org/10.1007/s11856-021-2278-y]]

//- 2022-02-18 &br;
//K.Umezu, The logistic elliptic equation with the nonlinear boundary condition arising from coast fishery harvesting, (2022), preprint. 
//[[arXiv:2202.09442:https://arxiv.org/abs/2202.09442]]

//- 2021-12-28 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results. '''Israel Journal of Mathematics''' (2021). [[https://doi.org/10.1007/s11856-021-2278-y:https://doi.org/10.1007/s11856-021-2278-y]]

//- 2021-08-04 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and positivity issues in a quasilinear indefinite problem, [['''Calculus of Variations and Partial Differential Equations''':https://www.springer.com/journal/526]], ''60'', Article number: 187 (2021).  [[10.1007/s00526-021-02057-8:https://doi.org/10.1007/s00526-021-02057-8]] 
 
// [[arXiv:2007.09498:https://arxiv.org/abs/2007.09498]]

//- 2021-07-30 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and sign properties of minimizers in a quasilinear indefinite problem, [['''Communications on Pure and Applied Analysis''':https://www.aimsciences.org/journal/1534-0392]], ''20''(6),  (2021), 2313--2322. 
//[[10.3934/cpaa.2021078:https://doi.org/10.3934/cpaa.2021078]]

// [[arXiv:2001.11318:https://arxiv.org/abs/2001.11318]]

//- 2021-07-19 &br;
//K.Umezu, Uniqueness of a positive solution for the Laplace equation with indefinite superlinear boundary condition, (2021), preprint. 
//[[arXiv:2107.07719:https://arxiv.org/abs/2107.07719]]

//- 2021-07-14 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and positivity issues in a quasilinear indefinite problem, [['''Calculus of Variations and Partial Differential Equations''':https://www.springer.com/journal/526]], (2021), accepted.  
//[[arXiv:2007.09498:https://arxiv.org/abs/2007.09498]]

//- 2021-04-14 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and sign properties of minimizers in a quasilinear indefinite problem, [['''Communications on Pure and Applied Analysis''':https://www.aimsciences.org/journal/1534-0392]], (2021), in press. 
// [[arXiv:2001.11318:https://arxiv.org/abs/2001.11318]]

//- 2021-03-30 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and sign properties of //minimizers in a quasilinear indefinite problem, (2021), accepted in 
//[['''Communications on Pure and Applied Analysis''':https://www.aimsciences.org/journal/1534-0392]]. //[[arXiv:2001.11318:https://arxiv.org/abs/2001.11318]]

//- 2021-01-17 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Past and recent contributions to indefinite sublinear elliptic problems (review article), 
//[['''Rendiconti dell'Istituto di Matematica dell'Universit&#224; di Trieste''':https://rendiconti.dmi.units.it/]], ''52''(1), (2020), 217--241. 
//[[10.13137/2464-8728/30913:https://doi.org/10.13137/2464-8728/30913]] 
// [[arXiv:2004.01284:https://arxiv.org/abs/2004.01284]]

//- 2020-11-20 &br; 
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results, [['''Israel Journal of Mathematics''':https://www.springer.com/journal/11856]], (2020), accepted. 
//[[arXiv:2001.09315:https://arxiv.org/abs/2001.09315]]

//- 2020-11-05 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Past and recent contributions to indefinite sublinear elliptic problems (review article), 
//[['''Rendiconti dell'Istituto di Matematica dell'Universit&#224; di Trieste''':https://rendiconti.dmi.units.it/]], ''52'', (2020). 
//[[10.13137/2464-8728/30913:https://doi.org/10.13137/2464-8728/30913]] 
//[[arXiv:2004.01284:https://arxiv.org/abs/2004.01284]]

//- 2020-07-19 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and positivity issues in a quasilinear indefinite problem, (2020), preprint. 
//[[arXiv:2007.09498:https://arxiv.org/abs/2007.09498]]

//- 2020-07-13 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Past and recent contributions to indefinite sublinear elliptic problems (review article), 
//[['''Rendiconti dell'Istituto di Matematica dell'Universit&#224; di Trieste''':https://rendiconti.dmi.units.it/]], (2020), in press. //[[arXiv:2004.01284:https://arxiv.org/abs/2004.01284]]

//- 2020-04-06 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Past and recent contributions to //indefinite sublinear elliptic problems (review article), preprint. [[	//arXiv:2004.01284:https://arxiv.org/abs/2004.01284]]

//- 2020-02-20 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem I: positivity, exact multiplicity, and existence of a subcontinuum, '''Annali di Matematica Pura ed Applicata(1923-)''', ''199''(5), (2020), 2015--2038.  
//[[10.1007/s10231-020-00954-x:https://doi.org/10.1007/s10231-020-00954-x]]

//[[arXiv:1901.04019:https://arxiv.org/abs/1901.04019]]

//- 2020-01-31 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and sign properties of //minimizers in a quasilinear indefinite problem, (2020), preprint. //[[arXiv:2001.11318:https://arxiv.org/abs/2001.11318]]

//- 2020-01-25 &br; 
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results, preprint. 
//[[arXiv:2001.09315:https://arxiv.org/abs/2001.09315]]

//- 2020-01-25 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem I: positivity, exact multiplicity, and existence of a subcontinuum, '''Annali di Matematica Pura ed Applicata''', (2020), in press. 
//[[arXiv:1901.04019:https://arxiv.org/abs/1901.04019]]

//- 2019-11-13 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, '''Discrete and Continuous Dynamical Systems-A''', ''40''(2), (2020), 817--845. 
//[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]
//[[10.3934/dcds.2020063:http://doi.org/10.3934/dcds.2020063]]

//- 2019-10-17 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, to appear in '''[[Discrete and  Continuous Dynamical Systems - A:https://www.aimsciences.org/journal/1078-0947]]''', ''40''(2), (2020). //[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]

//- 2019-08-30 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, accepted in '''[[Discrete and  Continuous Dynamical Systems:https://www.aimsciences.org/journal/1078-0947]]'''.  [[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]

//- 2019-05-04 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive //solutions for indefinite concave-convex problems, '''Advanced Nonlinear  //Studies''', ''19''(2), (2019), 391--412. 
//[[10.1515/ans-2018-2027:https://doi.org/10.1515/ans-2018-2027]]

//- 2019-02-27 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, '''Advances in Nonlinear Analysis''', ''8''(1), (2019), 175--192. 
//[[10.1515/anona-2016-0023:http://dx.doi.org/10.1515/anona-2016-0023]]

//- 2019-01-14 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear elliptic problem: positivity, exact multiplicity, and existence of a subcontinuum, preprint. //[[arXiv:1901.04019:https://arxiv.org/abs/1901.04019]]

// \href{https://arxiv.org/abs/1901.04019}{arXiv:1901.04019}

//- 2018-09-11 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, '''Advanced Nonlinear  Studies''', (2018), published online. DOI: [[10.1515/ans-2018-2027:https://doi.org/10.1515/ans-2018-2027]]

//- 2018-07-27 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, accepted in [['''Advanced Nonlinear Studies''':https://www.degruyter.com/view/j/ans]]. &nbsp; //(arXiv:1710.07802) &nbsp; Downloadable //[[pdf:https://arxiv.org/pdf/1710.07802.pdf]]

//- 2018-02-27 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity, 
//'''Nonlinear Differential Equations and Applications NoDEA''' (2018)  ''25'':12.

////////////////////////////////////
//- 2018-02-11&br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity, accepted in [['''Nonlinear Differential Equations and Applications NoDEA''':http://bit.ly/2EhPkpD]].
//&nbsp; (arXiv:1705.07791) &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1705.07791.pdf]]
//
//- 2018-02-02 &br; 
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, '''Communications on Pure and Applied Analysis''', ''17''(3), (2018), 1255-1269. &nbsp; &size(13){&color(red){[[''pdf'':https://arxiv.org/pdf/1610.00964v3.pdf]] with corrected figures for the published version};}; 
// DOI: [[10.3934/cpaa.2018060:http://dx.doi.org/10.3934/cpaa.2018060]] 
//(arXiv:1610.00964) 
//&nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1610.00964.pdf]]

////////////////////////////////////////////////////

//- 2017-12-16 &br; 
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, [['''Communications on Pure and Applied Analysis''':http://aimsciences.org/journal/1534-0392]], to be published in ''17''(3)(May 2018).  
//(arXiv:1610.00964) &nbsp; Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]

////////////////////////////////////////////////////////////////
//- 2017-10-24 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, preprint. &nbsp; //(arXiv:1710.07802) &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1710.07802.pdf]]

//////////////////////////////////
//- 2017-10-20 &br; 
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, [['''Communications on Pure and Applied Analysis''':https://www.aimsciences.org/journals/home.jsp?journalID=3]], to appear. 
//(arXiv:1610.00964) &nbsp; Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]

///////////////////////////////////
//- 2017-09-15 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, preprint.  //[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]

////////////////////////////////////////////////////
//- 2017-08-08 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, '''Journal of Differential Equations''', ''263''(8), (2017), 4481-4502. 
//DOI:
//[[10.1016/j.jde.2017.05.021:http://dx.doi.org/10.1016/j.jde.2017.05.021]]
//&nbsp; (arXiv:1610.07872) 
//&nbsp;  Downloadable [[pdf:https://arxiv.org/pdf/1610.07872.pdf]]

///////////////////////////////
//- 2017-07-10 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, '''Topological Methods in Nonlinear Analysis''', ''49''(2), (2017), 739-756. DOI: //[[10.12775/TMNA.2017.007:http://dx.doi.org/10.12775/TMNA.2017.007]] 
// &nbsp; (arXiv:1703.04229) &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]

///////////////////////////////////////////////////////

//- 2017-06-29 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, '''Israel Journal of Mathematics''', ''220''(1), (2017), 103-160. &nbsp; DOI: [[10.1007/s11856-017-1512-0:http://dx.doi.org/10.1007/s11856-017-1512-0]] 
//&nbsp;(arXiv:1603.04940). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]

////////////////////////////////////////
//- 2017-05-23 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity, preprint.
//&nbsp; (arXiv:1705.07791) &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1705.07791.pdf]]

////////////////////////////////////////////////////
//- 2017-05-21 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, '''Journal of Differential Equations''', (2017), Articles in Press. &nbsp;  DOI: [[10.1016/j.jde.2017.05.021:http://dx.doi.org/10.1016/j.jde.2017.05.021]]
//&nbsp; (arXiv:1610.07872) &nbsp;  Downloadable //[[pdf:https://arxiv.org/pdf/1610.07872.pdf]]

///////////////////////////////
//- 2017-05-17 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, '''Topological Methods in Nonlinear Analysis''', (2017), online first. DOI: [[10.12775/TMNA.2017.007:http://dx.doi.org/10.12775/TMNA.2017.007]] &nbsp; (arXiv:1703.04229) &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]

/////////////////////////////////////
//- 2017-05-05 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, '''Israel Journal of Mathematics''', (2017), first online. &nbsp; DOI: [[10.1007/s11856-017-1512-0:http://dx.doi.org/10.1007/s11856-017-1512-0]] &nbsp;
//(arXiv:1603.04940). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]

//--------------------------------------------------------------------
//- 2017-03-25 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, [['''Topological Methods in Nonlinear Analysis''':http://apcz.umk.pl/czasopisma/index.php/TMNA]], (2017), to appear (arXiv:1703.04229). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]

//>''Abstract'' We proceed with the investigation of the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  $$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Dealing now with the case $b \geq 0$, $b \not \equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of positive solutions of $(P_\lambda)$. Our approach is based on {\it a priori} bounds, a regularisation procedure, and Whyburn's topological method.

//-------------------------------------------------------------
//- 2017-03-23 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]], in press (arXiv:1603.04940). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]

//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.

//>''Abstract'' We investigate the problem $$ -\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  $$ where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.

//----------------------------------------------------------------------

//- 2017-02-03 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]], in press (arXiv:1603.04940). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]

//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.

//>''Abstract'' We investigate the problem $$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  $$where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.

//---------------------------------------------------------------------

//- 2016-12-02 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, '''Advances in Nonlinear Analysis''' (2016). online published. &nbsp; DOI: [[10.1515/anona-2016-0023:http://dx.doi.org/10.1515/anona-2016-0023]]
// スペ〖ス &nbsp; 染逞 &emsp; 链逞

//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & \mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & \mbox{on $\partial \Omega$}, \end{cases} \leqno{(P_\lambda)}$$ where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some $\alpha \in (0,1)$. We show that  $\int_{\partial \Omega} b <0$ is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.

//---------------------------------------------------------------

//- 2016-10-25 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, preprint (arXiv:1610.07872). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1610.07872.pdf]]

//>''Abstract'' We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity
//argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems.

////////////////
//- 2016-10-11 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, accepted in '''[[Advances in Nonlinear Analysis:https://www.degruyter.com/view/j/anona]]''' (2016).

//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & //\mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & //\mbox{on $\partial \Omega$},
//\end{cases} \leqno{(P_\lambda)}  
//$$
//where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some $\alpha \in (0,1)$. We show that  $\int_{\partial \Omega} b <0$ is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.

//-----------------------------------------------------------------

//- 2016-09-01 &br; 
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative //solutions set of an indefinite elliptic problem, preprint. //(arXiv:1610.00964) &nbsp; Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]

//>''Absract.''  We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with homogeneous Neumann boundary conditions. This result complements our previous work, where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory,   rescaling and regularising arguments, a priori bounds, and Whyburn's topological method.

////////
//- 2016-07-27 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite 
//equation with a nonlinear boundary condition: existence, multiplicity and //asymptotic profiles, '''Calculus of Variations and PDEs''', (2016). //http://dx.doi.org/10.1007/s00526-016-1033-4

//>''Abstract.''  We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a positive parameter $\lambda$, which is inversely proportional to the diffusion rate. We establish several multiplicity results when the diffusion rate is large and analyze the asymptotic profiles and the stability properties of these steady states as the diffusion rate grows to infinity. In particular, our results show that in some cases bifurcation from zero and from infinity occur at $\lambda=0$. Our approach combines variational and bifurcation techniques.

//----------------------------------------------------------------------

//- 2016-07-18 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, [['''Topological Methods in Nonlinear Analysis''':http://apcz.umk.pl/czasopisma/index.php/TMNA]], in press (arXiv:1703.04229). &nbsp; Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]

//>''Abstract'' We proceed with the investigation of the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  $$where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Dealing now with the case $b \geq 0$, $b \not \equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of positive solutions of $(P_\lambda)$. Our approach is based on {\it a priori} bounds, a regularisation procedure, and Whyburn's topological method.

//---------------------------------------------------------------
//- 2016-06-05 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite 
//equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, accepted in [['''Calculus of Variations and PDEs''':http://www.springer.com/mathematics/analysis/journal/526]]. 
//[[arXiv:1509.01753:http://arxiv.org/abs/1509.01753]]

//-------------------------------------------------------------------
//- 2016-05-20 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, accepted in [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]]. //[[arXiv:1603.04940:http://arxiv.org/abs/1603.04940]]

//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.

//>''Abstract'' We investigate the problem 
//$$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad //\frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  //$$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.

//---------------------------------------------------------
//- 2016-04-22 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, preprint.

//------------------------------------------------------------------
//- 2016-03-17 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, preprint. [[arXiv:1603.04940:http://arxiv.org/abs/1603.04940]]

//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.

//>''Abstract'' We investigate the problem 
//$$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad //\frac{\partial u}{\partial \n} = 0  \mbox{ on } \partial \Omega, \leqno{(P_\lambda)}  $$ 
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), //$1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as //$\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.

//--------------------------------------------------------------------------

//- 2016-01-25 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, preprint.

//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & //\mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & //\mbox{on $\partial \Omega$},
//\end{cases} \leqno{(P_\lambda)}  
//$$
//where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some //$\alpha \in (0,1)$. We show that  $\int_{\partial \Omega} b <0$
//is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.

//--------------------------------------------------------------------
//- 2015-09-15 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, '''Annali di Matematica Pura ed Applicata''', (2015). http://dx.doi.org/10.1007/s10231-015-0531-x

//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Brezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.

//---------------------------------------------------------------------
//- 2015-09-09 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, [[arXiv:1509.01753:http://arxiv.org/abs/1509.01753]]

//--------------------------------------------------------------
//- 2015-08-25 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, to appear in '''Annali di Matematica Pura ed Applicata''' (2015).

//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Br\'ezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.

//--------------------------------------------------------------------
//- 2015-07-08 &br;
//K. Taira and K. Umezu, Bifurcation for nonlinear elliptic boundary value problems IV, preprint.

//>''Abstract'' This paper is devoted to global static bifurcation theory for a class of '''degenerate''' boundary value problems for semilinear second-order elliptic differential operators, generalizing the authors' previous work.  More precisely, we prove global bifurcation for positive solutions of a degenerate logistic like equation with a smooth linear combination of the Dirichlet and Neumann boundary conditions.  In the proof we make use of the super-subsolution method to prove existence and uniqueness theorems of positive solutions of our semilinear elliptic boundary value problems.  The approach here is based on the uniqueness of a bifurcation point and the uniqueness of a bifurcation solution curve.

//---------------------------------------------------------------------
//- 2015-05-06 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, preprint.

//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Br\'ezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.

//---------------------------------------------------------------------
//- 2015-04-14 &br;
//H. Ramos Quoirin and K. Umezu, Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case, '''J. Math. Anal. Appl.''' ''428'', (2015), 1265-1285. http://dx.doi.org/10.1016/j.jmaa.2015.04.005

//>''Abstract.'' We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work (H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation, J. Differential Equations 257, (2014), 3935-3977.), where the case of sign-changing nonlinear boundary conditions is considered.

//------------------------------------------------------------------------
//- 2014-12-24 &br;
//H. Ramos Quoirin and K. Umezu, Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case, submitted.

//---------------------------------------------------------------------
//- 2014-10-01 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation, '''J. Differential Equations''' ''257'', (2014), 3935-3977.

//[[doi.org/10.1016/j.jde.2014.07.016:http://dx.doi.org/10.1016/j.jde.2014.07.016]]

//>''Abstract.'' We investigate a semilinear elliptic equation with a logistic nonlinearity and an indefinite nonlinear boundary condition, both depending on a parameter. Overall, we analyze the effect of the indefinite nonlinear boundary condition on the structure of the positive solution set. Based on variational and bifurcation techniques, our main results establish the existence of '''three''' nontrivial non-negative solutions for some values of the parameter, as well as their asymptotic behavior. These results suggest that the positive solution set contains an '''S-shaped component''' in some case, as well as a combination of a C-shaped and a S-shaped components, called a '''CS-shaped component''', in another case.

//------------------------------------------------------------------------
//- 2014-09-07 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, preprint.

//- 2014-08-22 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary //conditions on the structure of the positive solutions set of a logistic //equation, JDE(2014), //[[doi.org/10.1016/j.jde.2014.07.016:http://dx.doi.org/10.1016/j.jde.2014.07.016]]

//- 2014-08-12 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary //conditions on the structure of the positive solution set of a logistic //equation, JDE(2014), in press.

//- 2013-06-17 &br; 
//K.Umezu, Global structure of supercritical bifurcation with turning points 
//for the logistic elliptic equation with nonlinear boundary conditions, //'''Nonlinear Analysis''', ''89'', (2013), 250-266.   //[[doi:10.1016/j.na.2013.05.011:http://dx.doi.org/10.1016/j.na.2013.05.011]]

//- 2013-05-23 &br; 
//附哼·榜倦络池兜伴池婶眶池兜伴兜技では &nbsp; &size(20){节兜鉴∈傣部池∷
//の给//淑}; &nbsp; をしております∈涅磊2013钳6奉24泣(久磅铜跟)〃&nbsp; 
//2013钳10//奉1泣何脱徒年∷ˉ给淑掘凤霹拒嘿は布淡のリンク黎をご徊救
//くださいˉご//炳淑くださいますよう·よろしくお搓い拷し惧げますˉ
//&br; 
//> http://www.ibaraki.ac.jp/employment/index.html

//Bifurcation approach to a logistic elliptic 
//equation with a homogeneous incoming flux boundary condition, 
//'''J. Differential Equations''', ''252'',(2012), 1146-1168.  //[[doi:10.1016/j.jde.2011.08.043:http://dx.doi.org/10.1016/j.jde.2011.08.043]] 
//
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//ⅸ310-8512 垮竿辉矢叠2-1-1 榜倦络池兜伴池婶眶池兜伴兜技 &br;
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