Abstract and Applied Analysis
Volume 2013 (2013), Article ID 624352, 5 pages
http://dx.doi.org/10.1155/2013/624352
Research Article

A Lotka-Volterra Competition Model with Cross-Diffusion

Wenyan Chen and Ya Chen

Department of Mathematics, Southeast University, Nanjing 210018, China

Received 9 October 2012; Revised 24 January 2013; Accepted 29 January 2013

Academic Editor: Lan Xu

Copyright © 2013 Wenyan Chen and Ya Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.