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March  2003, 2(1): 65-76. doi: 10.3934/cpaa.2003.2.65

Positive solutions for a class of reaction-diffusion systems

A. Dall'Acqua 1,

1. 

Department of Applied Analysis, Delft University of Technology, P.O.box 5031, 2600CD Delft, Netherlands

Received  July 2002 Revised  November 2002 Published  December 2002

In this paper we will derive existence of positive solutions for a system of two coupled superlinear elliptic equations with Dirichlet boundary condition. We will use a topological method; in fact the class of systems that we will study does not allow a variational approach. After establishing an a priori estimate for the solutions, we will obtain existence by a continuation method.
Keywords: continuation method., Hardy-Sobolev inequality, Reaction-diffusion systems, a priori estimates.
Mathematics Subject Classification: 35J60, 35J45, 35B4.
Citation: A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65
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