Positive solutions for a class of reaction-diffusion systems

A. Dall'Acqua

doi:10.3934/cpaa.2003.2.65

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2003, Volume 2, Issue 1: 65-76. Doi: 10.3934/cpaa.2003.2.65

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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

Received: July 2002

Revised: November 2002

Published: November 2003

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Abstract

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.

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Mathematics Subject Classification: 35J60, 35J45, 35B45.

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