STABLE COEXISTENCE IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION.

Chris Cosner, A. C. Lazer

Research output: Contribution to journalArticle

132 Scopus citations

Abstract

We study the existence, uniqueness, and stability of coexistence states in the Lotka-Volterra model with diffusion for two competing species. We assume that the parameters describing the interaction and self-limitation of the species are constant, and consider two types of growth and boundary conditions: periodic growth rates with Neumann boundary conditions, and constant growth rates with Dirichlet boundary conditions. The main tools for our investigations are existence and comparison theorems based on the maximum principle, upper and lower solutions, and the variational characterization of eigenvalues.

Original languageEnglish (US)
Pages (from-to)1112-1132
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume44
Issue number6
DOIs
StatePublished - Jan 1 1984

ASJC Scopus subject areas

  • Applied Mathematics

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