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

Published online by Cambridge University Press:  01 July 2004

Kenichiro Umezu
Kenichiro Umezu
Affiliation:
Faculty of Engineering, Maebashi Institute of Technology, Maebashi 371-0816, Japan ([email protected])
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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

Keywords

bifurcation equationssecondary bifurcationconstrained minimization problemspositive solutionsmultiplicity resultspopulation dynamics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 495 - 512
Copyright
Copyright © Edinburgh Mathematical Society 2004