Existence of Solutions for a Quasilinear Reaction Diffusion System

Canrong Tian

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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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https://doi.org/10.1155/2012/368425

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:368425

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