Abstract and Applied Analysis

A Lotka-Volterra Competition Model with Cross-Diffusion

Wenyan Chen and Ya Chen

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Abstract

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 624352, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449858

Digital Object Identifier
doi:10.1155/2013/624352

Mathematical Reviews number (MathSciNet)
MR3035235

Zentralblatt MATH identifier
1276.92099

Citation

Chen, Wenyan; Chen, Ya. A Lotka-Volterra Competition Model with Cross-Diffusion. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 624352, 5 pages. doi:10.1155/2013/624352. https://projecteuclid.org/euclid.aaa/1393449858


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