A singular elliptic system involving the p(x)-Laplacian and generalized Lebesgue–Sobolev spaces

Abstract

The purpose of this work is to study a class of singular elliptic system involving the [Formula: see text]-Laplace operator of the form [Formula: see text] where [Formula: see text] [Formula: see text] is a bounded domain with [Formula: see text] boundary, [Formula: see text] are two parameters, [Formula: see text] are non-negative weight functions with compact support in [Formula: see text] and [Formula: see text] 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.