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Positive solution for a class of coupled (p,q)-Laplacian nonlinear systems

Eder M Martins* and Wenderson M Ferreira

Author Affiliations

Departamento de Matemática, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35.400-000, Brazil

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Boundary Value Problems 2014, 2014:21  doi:10.1186/1687-2770-2014-21

Published: 20 January 2014

Abstract

In this article, we prove the existence of a nontrivial positive solution for the elliptic system

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M2">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M3">View MathML</a> denotes the p-Laplacian operator, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M4">View MathML</a> and Ω is a smooth bounded domain in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M5">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/21/mathml/M6">View MathML</a>). The weight functions ω and ρ are continuous, nonnegative and not identically null in Ω, and the nonlinearities f and g are continuous and satisfy simple hypotheses of local behavior, without involving monotonicity hypotheses or conditions at ∞. We apply the fixed point theorem in a cone to obtain our result.

MSC: 35B09, 35J47, 58J20.