Asymptotically stable equilibria for monotone semiflows

M. W. Hirsch, Hal Smith

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 2006

Fingerprint

Semiflow
Asymptotically Stable
Partial differential equations
Monotone
Kolmogorov System
Competition System
Parabolic Partial Differential Equations
Analyticity
Finiteness
Semilinear
Compactness
Subset

Keywords

  • Analytic semiflow
  • Asymptotically stable equilibria
  • Kolmogorov competition system
  • Order preserving semiflow

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Asymptotically stable equilibria for monotone semiflows. / Hirsch, M. W.; Smith, Hal.

In: Discrete and Continuous Dynamical Systems, Vol. 14, No. 3, 03.2006, p. 385-398.

Research output: Contribution to journalArticle

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