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[[FrontPage]] [[English Page]] #contents * Journal Papers refereed [#bc80d942] /////////////////////////////////////////////////////////////// - K. Umezu, Blowing-up of principal eigenvalues for Neumann boundary conditions, accepted in '''[[Proc. Roy. Soc. Edinburgh Sect. A.:http://www.ingentaconnect.com/content/rse/proca]]''' >''Abstract'': This paper studies blowing-up properties of a unique positive principal eigenvalue for a linear elliptic eigenvalue problem with an indefinite weight function and Neumann boundary condition. Necessary and sufficient conditions for the blowing-up are discussed, based on the variational characterization of the unique positive principal eigenvalue. A counterexample is constructed, which shows that a known necessary and sufficient condition for the blowing-up in the Dirichlet boundary condition case no longer remains true in the Neumann one. /////////////////////////////////////////////////////////////////// - K. Umezu, On eigenvalue problems with Robin type boundary conditions having indefinite coefficients, accepted in '''[[Applicable Analysis:http://www.tandf.co.uk/journals/titles/00036811.asp]]'''. >''Abstract'': A Robin type boundary condition with a sign-changing coefficient is treated. First the associated linear elliptic eigenvalue problem is studied, where the existence of a principal eigenvalue is discussed by use of a variational approach. Secondly the associated semilinear elliptic boundary value problem of logistic type is studied and the one parameter-dependent structure of positive solutions is investigated, where results obtained are due to the construction of suitable super and subsolutions by using the principal positive eigenfunctions of the linear eigenvalue problem. //////////////////////////////////////////////////////////////////// - K. Umezu, Multiplicity of positive solutions under nonlinear boundary conditions for diffusive logistic equations, '''[[Proc. Edinburgh Math. Soc.:http://journals.cambridge.org/action/displayJournal?jid=PEM]]''' ''47''(2) (2004), pp.495-512. >''Abstract'': In this paper we consider the existence and multiplicity of positive solutions of a nonlinear elliptic boundary value problem with nonlinear boundary conditions which arises in population dynamics. While bifurcation problems from lines of trivial solutions are studied, the existence of bifurcation positive solutions from infinity is discussed. The former will be caught by the reduction to a bifurcation equation following the Lyapunov and Schmidt procedure. The latter will be based on a variational argument depending on the corresponding constrained minimization problem. ////////////////////////////////////////////////////////////////// - K. Umezu, Local bifurcation analysis and stability of steady-state solutions of diffusive logistic equations with nonlinear boundary conditions, '''[[Communications in Applied Analysis:http://www.dynamicpublishers.com/dynamic.htm]]''' ''8''(4) (2004), pp.533-547. - K. Umezu, Behavior and stability of positive solutions of nonlinear elliptic boundary value problems arising in population dynamics, '''[[Nonlinear Anal.:http://www.elsevier.com/wps/find/journaldescription.cws_home/239/description]]''' ''49''(6) (2002), pp.817-840. - K. Umezu, Bifurcation from infinity for asymptotically linear elliptic eigenvalue problems, '''[[J. Math. Anal. Appl.:http://www.elsevier.com/wps/find/journaldescription.cws_home/622886/description#description]]''' ''267''(2)(2002), pp.651-664. - K. Umezu, Nonlinear elliptic boundary value problems suggested by fermentation, '''[[Nonlinear Differential Equations Appl.(NoDEA):http://www.springerlink.com/(wf3zsa45hohlilr0exzzml55)/app/home/journal.asp?referrer=parent&backto=linkingpublicationresults,1:101200,1]]''' ''7''(2) (2000), pp.143-155. - K. Umezu, Global positive solution branches of positone problems with nonlinear boundary conditions, '''[[Differential Integral Equations:http://www.aftabi.com/DIE/die.html]]''' ''13''(4-6) (2000), pp.669-686. - K. Umezu, Multiplicity of positive solutions to semilinear elliptic boundary value problems, '''[[Abstr. Appl. Anal.:http://www.hindawi.com/journals/aaa/]]''' ''4''(3) (1999), pp. 195-208. - K. Umezu, Positive solutions of a forced nonlinear elliptic boundary value problem, '''[[J. Math. Soc. Japan:http://www.kurims.kyoto-u.ac.jp/~jmsj/JMSJ.htm]]''' ''51''(4) (1999), pp.801-815. - K. Umezu and K. Taira, Growing-up positive solutions of semilinear elliptic boundary value problems, '''[[J. Math. Anal. Appl.:http://www.elsevier.com/wps/find/journaldescription.cws_home/622886/description#description]]''' ''238''(1) (1999), pp.196-215. - K. Taira and K. Umezu, Semilinear elliptic boundary value problems in chemical reactor theory, '''[[J. Differential Equations:http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6866&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=df7b3e2c6f279d60249c1cc43c456765]]''' ''142''(2) (1998), pp.434-454. - K. Taira and K. Umezu, Positive solutions of sublinear elliptic boundary value problems, '''[[Nonlinear Anal.:http://www.elsevier.com/wps/find/journaldescription.cws_home/239/description]]'''. ''29''(7) (1997), pp.761-771. - K. Taira and K. Umezu, Bifurcation for nonlinear elliptic boundary value problems II, '''[[Tokyo J. Math.:http://www.tokyojm.jp/]]''' ''19''(2) (1996), pp.387-396. - K. Taira and K. Umezu, Bifurcation for nonlinear elliptic boundary value problems III, '''[[Adv. Differential Equations:http://www.aftabi.com/ADE/ade.html]]''' ''1''(4) (1996), pp.709-727. - K. Umezu, L^p-approach to mixed boundary value problems for second-order elliptic operators, '''[[Tokyo J. Math.:http://www.tokyojm.jp/]]''' ''17''(1) (1994), pp.101-123. - K. Umezu, On the Cauchy problem for analytic semigroups with weak singularity, '''[[Tsukuba J. Math.:http://www.math.tsukuba.ac.jp/~journal/tjm/tjm.html]]''' ''15''(2) (1991), pp.275-292. * Proceeding Papers refereed [#n1111035] - K. Umezu, '''Non-existence of positive solutions for diffusive logistic equations with nonlinear boundary conditions''', Progress in Nonlinear Differential Equations and Their Applications, Vol.64, 497-507, Birkhauser, Basel/Switzerland, 2005. - K. Umezu, '''One parameter-dependent nonlinear elliptic boundary value problems arising in population dynamics''', Advances in analysis, 177--186, World Sci. Publ., Hackensack, NJ, 2005. - K. Umezu, '''Bifurcation analysis in diffusive logistic equations with nonlinear boundary conditions''', Progress in analysis, Vol. I, II (Berlin, 2001), 1135--1141, World Sci. Publishing, River Edge, NJ, 2003. - K. Umezu, '''Bifurcation in population dynamics''', Elliptic and parabolic problems (Rolduc/Gaeta, 2001), 485-493, World Sci. Publishing, River Edge, NJ, 2002. - K. Taira and K. Umezu, '''Stability in chemical reactor theory''', Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998), 421-433, Lecture Notes in Pure and Appl. Math., 215, Dekker, New York, 2001 - K. Umezu and K. Taira, '''Positive solutions of semilinear elliptic boundary value problems in chemical reactor theory''', Direct and inverse problems of mathematical physics (Newark, DE, 1997), 415-422, Int. Soc. Anal. Appl. Comput., 5, Kluwer Acad. Publ., Dordrecht, 2000. * List of Presentations by Talks [#ea5df1a9] ////////////////////////////////////////////////////////////////// ** Talks in International Conferences [#ee952a42] - [[The first China-Japan Colloquium of Mathematical Biology (CJCMB):http://cjcmb.swu.edu.cn/First%20announcement.htm]], '''Blowing-up behavior of principal eigenvalues for Neumann boundary conditions''', Southwest University, Beibei, Chongqing, People's Republic of China, 24-28 April 2006 (scheduled). - ISAAC05, the 5th Congress, '''Elliptic eigenvalue problems with indefinite Robin boundary conditions''', University of Catania, Italy, 25-30 July 2005. - Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann, '''Existence and nonexistence of positive solutions for a semilinear elliptic problem arising in population dynamics''', University of Zurich, Zurich, 28-30 June 2004. - ISAAC03, the 4th Congress, '''On diffusive logistic equations having nonlinear boundary conditions''', York University, Toronto, 11-16 August 2003. - International Conference on Nonlinear Partial Differential Equations Theory and Approximation, '''Bifurcation problem for a semilinear elliptic equation arising in population dynamics, having nonlinear boundary conditions''', City University of Hong Kong, Hong Kong, 29 August - 2 September 2002. - The 4th European Conference on Elliptic and Parabolic Problems, '''Bifurcation in population dynamics''', Gaeta, Italy, 24-28 September 2001. - ISAAC01, the 3rd Congress, '''Bifurcation analysis in diffusive logistic equations with nonlinear boundary conditions''', Freie University, Berlin, 20-25 August 2001. - International Conference on Nonlinear Partial Differential Equations 99, '''Bifurcation and stability for diffusive logistic equations with nonlinear boundary conditions''', Lviv State University, Ukraine, 24-28 August 1999. - ICIAM 99, the 4th Congress, '''Elliptic boundary value problems with nonlinear boundary conditions''', University of Edinburgh, Scotland, 5-9 July 1999. - ISAAC97, the 1st Congress, '''Semilinear elliptic boundary value problems in chemical reactor theory''', University of Delaware, USA, 3-6 June 1997. ** Talks in Meetings of MSJ [#j47479f2] - Mar. 2006, 符号不定な重み係数をもつロバン型境界条件に対する 主固有値の特徴付け, 日本数学会'06年会函数方程式論分科会（中央大学理工学部）． - Mar. 2005, An estimate for turning points in sublinear elliptic boundary value problems, 日本数学会'05年会函数方程式論分科会（日本大学理工学部）． - Sep. 2003, Existence and limiting behavior of positive solutions for diffusive logistic equations with nonlinear flux on the boundary, 日本数学会'03総合分科会函数方程式論分科会（千葉大学理学部） - Mar. 2002, Global subcontinua arising in population dynamics, 日本数学会'02年会函数方程式論分科会（明治大学理工学部）． - Mar. 2001, Bifurcation in Population Genetics, 日本数学会'01年会函数方程式論分科会（慶應義塾大学理工学部）． - Mar. 2000, Bifurcation from infinity and uniqueness of positive solutions to semilinear elliptic equations with nonlinear boundary conditions, 日本数学会'00年会函数方程式論分科会（早稲田大学理工学部）． - 30 Mar. 2000, 非線形境界条件における人口動態モデルの正値解の挙動， 日本数学会'00年会函数方程式論分科会（早稲田大学理工学部）． - Mar. 1999, 化学反応論における漸近安定性, 日本数学会'99春年会函数方程式論分科会（学習院大学理学部）． - Oct. 1998, Positive solutions of semilinear elliptic boundary value problems, 日本数学会'98秋季函数方程式論分科会（大阪大学理学研究科）． - Mar. 1998, 化学反応論における安定性, 日本数学会'98年会函数方程式論分科会（名城大学理学部）． - Apr. 1997, 化学反応論における半線型楕円型境界値問題, 日本数学会'97年会函数方程式論分科会（信州大学理学部）． - Apr. 1996, 半線形楕円型境界値問題の正値解の一意存在定理, 日本数学会'96年会函数方程式論分科会（新潟大学理学部）． - Sep. 1995, 非線形楕円型境界値問題の正値解の一意存在定理, 日本数学会'95秋季函数方程式論分科会（東北大学理学部）． - Mar. 1995, 非線形楕円型境界値問題の解の分岐定理, 日本数学会'95年会函数方程式論分科会（立命館大学理工学部）． - Sep. 1993, ２階楕円型作用素に対する混合型境界値問題の $L^p$ アプローチ, 日本数学会'93秋季函数方程式論分科会（大阪府立大学総合科学部），１９９３年９月． * Others [#j7b7469e] - 科学研究費「人口動態論から要請された非線形楕円型境界値問題の正値解に対する定性的研究」基盤研究(C)(2), No.16540165, 平成16-18. - The ISAAC Award for Young Scientists, the International Society for Analysis, its Applications and Computation, August 2003.