Abstract
The purpose of this work is to study a class of singular elliptic system involving the p(x)-Laplace operator of the form
{-Delta(p(x))u = lambda(a)(x)vertical bar u vertical bar q((x)-2) + 1-a(x)/2 - alpha(x) - beta(x)c(x)vertical bar u vertical bar(-alpha(x))vertical bar nu vertical bar(1-beta(x)) in Omega,
-Delta(p(x))v = mu b(x)vertical bar v vertical bar(q(x)-2)v(x) + 1-beta(x)/2 - alpha(x) - beta(x)c(x)vertical bar u vertical bar(1-alpha(x))vertical bar v vertical bar(-beta(x)) in Omega,
u = v = 0, in partial derivative Omega,
where Omega subset of R-N, (N >= 2) is a bounded domain with C-2 boundary, lambda, mu are two parameters, a, b, c is an element of C(Omega) are non-negative weight functions with compact support in Omega and p, q, alpha, beta is an element of C((Omega) over bar) are assumed to satisfy the assumptions (A0)-(A2) in Sec. 1. We employ the Nehari manifold approach combined with some variational techniques in order to show the existence and the multiplicity of positive solutions.