Positive solution for a class of coupled
-Laplacian nonlinear systems
Departamento de Matemática, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35.400-000, Brazil
Boundary Value Problems 2014, 2014:21 doi:10.1186/1687-2770-2014-21Published: 20 January 2014
In this article, we prove the existence of a nontrivial positive solution for the elliptic system
where denotes the p-Laplacian operator, and Ω is a smooth bounded domain in (). 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.