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

Abstract

In this article, we prove the existence of a nontrivial positive solution for the elliptic system ⎧⎨ ⎩ –_pu = ω(x)f (v) in_, –_qv = ρ(x)g(u) in_, (u, v) = (0,0) on ∂_, where_p denotes the p-Laplacian operator, p, q > 1 and _ is a smooth bounded domain in RN (N ≥ 2). The weight functions ω and ρ are continuous, nonnegative and not identically null in _, 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