On the uniqueness of the positive steady state for Lotka-Volterra models with diffusion

S. W. Ali, George Cosner

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We give criteria for the uniqueness and stability of the componentwise positive steady state for the diffusive Lotka-Volterra model of several competing species under Dirichlet boundary conditions, thereby extending known results for cases of only two species. In the case of an underlying spatial domain which is one dimensional interval, we obtain an estimate for a quantity occurring in the hypotheses of a number of uniqueness results. The estimate sharpens those results and gives a partial negative answer to a conjecture of Korman and Leung.

Original languageEnglish (US)
Pages (from-to)329-341
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume168
Issue number2
DOIs
StatePublished - 1992

Fingerprint

Lotka-Volterra Model
Uniqueness
Boundary conditions
Competing Species
Estimate
Dirichlet Boundary Conditions
Partial
Interval

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On the uniqueness of the positive steady state for Lotka-Volterra models with diffusion. / Ali, S. W.; Cosner, George.

In: Journal of Mathematical Analysis and Applications, Vol. 168, No. 2, 1992, p. 329-341.

Research output: Contribution to journalArticle

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