Abstract and Applied Analysis

A Lotka-Volterra Competition Model with Cross-Diffusion

Wenyan Chen and Ya Chen

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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.

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

First available in Project Euclid: 26 February 2014

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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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