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

George Cosner, A. C. Lazer

Research output: Contribution to journalArticle

130 Citations (Scopus)

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
StatePublished - Dec 1984

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Lotka-Volterra Model
Competition Model
Coexistence
Coexistence States
Boundary conditions
Competing Species
Upper and Lower Solutions
Comparison Theorem
Growth Conditions
Neumann Boundary Conditions
Maximum Principle
Existence Theorem
Dirichlet Boundary Conditions
Existence and Uniqueness
Maximum principle
Eigenvalue
Interaction

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

STABLE COEXISTENCE IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION. / Cosner, George; Lazer, A. C.

In: SIAM Journal on Applied Mathematics, Vol. 44, No. 6, 12.1984, p. 1112-1132.

Research output: Contribution to journalArticle

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