The Nehari manifold for a degenerate elliptic equation involving a sign-changing weight function

This paper is concerned with a degenerate elliptic equation of the form {-div(vertical bar x vertical bar(-2a) del u) = vertical bar x vertical bar(-2b) vertical bar u vertical bar(p-1) u + lambda f(x)vertical bar x vertical bar(-2c) vertical bar u vertical bar(q-1) u in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N (N >= 3) is an open bounded domain with smooth boundary, 0 is an element of Omega, 0 < a < N-2/2, a <= b, c < a + 1 and b = c(p+ 1)/q+ 1, f is an element of C(<(Omega)over bar>) be a sign- changing weight function. Using the Nehari manifold and a fibering map, the existence of multiple nonnegative solutions is established. (C) 2011 Elsevier Ltd. All rights reserved.