MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS

Kenichiro Umezu

doi:10.1017/S0013091503000294

Abstract

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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.

AMS 2000 Mathematics subject classification: Primary 35J65; 35J20; 35P30; 35B32; 92D25

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Umezu, Kenichiro 2005. Nonlinear Elliptic and Parabolic Problems. Vol. 64, Issue. , p. 497.

Umezu, Kenichiro 2012. Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition. Journal of Differential Equations, Vol. 252, Issue. 2, p. 1146.

Umezu, Kenichiro 2013. Global structure of supercritical bifurcation with turning points for the logistic elliptic equation with nonlinear boundary conditions. Nonlinear Analysis: Theory, Methods & Applications, Vol. 89, Issue. , p. 250.

Ramos Quoirin, Humberto and Umezu, Kenichiro 2015. Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case. Journal of Mathematical Analysis and Applications, Vol. 428, Issue. 2, p. 1265.

Madeira, Gustavo Ferron and do Nascimento, Arnaldo Simal 2016. Bifurcation of stable equilibria under nonlinear flux boundary condition with null average weight. Journal of Mathematical Analysis and Applications, Vol. 441, Issue. 1, p. 121.

Liu, Ping and Shi, Junping 2018. Bifurcation of positive solutions to scalar reaction–diffusion equations with nonlinear boundary condition. Journal of Differential Equations, Vol. 264, Issue. 1, p. 425.

Ramos Quoirin, Humberto and Umezu, Kenichiro 2019. An elliptic equation with an indefinite sublinear boundary condition. Advances in Nonlinear Analysis, Vol. 8, Issue. 1, p. 175.

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Article contents

MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS

Abstract

Keywords

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