Existence of Solutions for a Quasilinear Reaction Diffusion System

Canrong Tian

Abstract and Applied Analysis, 2012, vol. 2012, 1-14

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:368425

DOI: 10.1155/2012/368425

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