Asymptotically stable equilibria for monotone semiflows

M. W. Hirsch; Hal Smith

doi:10.3934/dcds.2006.14.385

Asymptotically stable equilibria for monotone semiflows

M. W. Hirsch, Hal Smith

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Conditions for the existence of a stable equilibrium and for the existence of an asymptotically stable equilibrium for a strongly order preserving semiflow are presented. Analyticity of the semiflow and the compactness of certain subsets of the set of equilibria are required for the latter and yield finiteness of the equilibrium set. Our results are applied to semilinear parabolic partial differential equations and to the classical Kolmogorov competition system with diffusion.

Original language	English (US)
Pages (from-to)	385-398
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems
Volume	14
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2006.14.385
State	Published - Mar 2006

Keywords

Analytic semiflow
Asymptotically stable equilibria
Kolmogorov competition system
Order preserving semiflow

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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AB - Conditions for the existence of a stable equilibrium and for the existence of an asymptotically stable equilibrium for a strongly order preserving semiflow are presented. Analyticity of the semiflow and the compactness of certain subsets of the set of equilibria are required for the latter and yield finiteness of the equilibrium set. Our results are applied to semilinear parabolic partial differential equations and to the classical Kolmogorov competition system with diffusion.

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KW - Order preserving semiflow

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Asymptotically stable equilibria for monotone semiflows

Abstract

Keywords

ASJC Scopus subject areas

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