THE FIBERING MAP APPROACH TO A p(x)-LAPLACIAN EQUATION WITH SINGULAR NONLINEARITIES AND NONLINEAR NEUMANN BOUNDARY CONDITIONS

The purpose of this paper is to study the singular Neumann problem involving the p(x)-Laplace operator: (p(lambda)) {-Delta(p(x))u+vertical bar u vertical bar(p(x)-2)(u)=lambda a(x)/u(delta)(x) in Omega, u > 0 in Omega, vertical bar del u vertical bar(p(x)-2)partial derivative u/partial derivative v=b(x)u(q(x)-2)u on partial derivative Omega, where Omega subset of R-N, N >= 2, is a bounded domain with C-2 boundary, lambda is a positive parameter, a, b is an element of C (Omega) over bar are non-negative weight functions with compact support in Omega and delta(x), p(x), q(x) is an element of C (Omega) over bar are assumed to satisfy the assumptions (A0)-(A1) in Section 1. We employ the Nehari manifold approach and some variational techniques in order to show the multiplicity of positive solutions for the p(x)-Laplacian singular problems.