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Abstract and Applied Analysis
Volume 2012, Article ID 368425, 14 pages
http://dx.doi.org/10.1155/2012/368425
Research Article

Existence of Solutions for a Quasilinear Reaction Diffusion System

Department of Basic Sciences, Yancheng Institute of Technology, Jiangsu, Yancheng 224003, China

Received 26 February 2012; Revised 30 April 2012; Accepted 30 April 2012

Academic Editor: D. Anderson

Copyright © 2012 Canrong Tian. 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

The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is applied to a Lotka-Volterra predator-prey model.