Asymptotically stable equilibria for monotone semiflows

M. W. Hirsch, Hal Smith

Research output: Contribution to journalArticle

13 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 languageEnglish (US)
Pages (from-to)385-398
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume14
Issue number3
DOIs
StatePublished - Mar 1 2006

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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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