On the existence of positive solution for a class of singular systems involving quasilinear operators

In this paper we consider the existence of positive solution for the following class of singular systems {-Delta(p)u = 1/v(1) + v(alpha 71), -Delta(q)v = 1/u(2) + u(alpha 72) in Omega, u, v > 0 in Omega, u = v = 0 on partial derivative Omega, where Omega subset of R-N, N >= 2, is a smooth bounded domain, Delta(p) and Delta(q) are, respectively, the p-Laplacian and q-Laplacian, with p, q > 1, and alpha(1), alpha(2), gamma(1) and gamma(2) are positive constants. The main tools used are a result due to Rabinowitz and a Hardy-Sobolev inequality. (c) 2006 Elsevier Inc. All rights reserved.