Variational eigenvalues of degenerate eigenvalue problems for the weighted p-Laplacian

We prove the existence of nondecreasing sequences of positive eigenvalues of the homogeneous degenerate quasilinear eigenvalue problem - div(a(x)vertical bar del u vertical bar(p-2)del u) = lambda b(x) vertical bar u vertical bar(p-2)u, lambda > 0 subject to Dirichlet boundary conditions on a bounded domain Omega. The diffusion coefficient a(x) is a function in L-loc(1)(Omega) and b(x) is a nontrivial function in L-r(Omega) (r depending on a, p and N) and may change sign. We use Ljusternik-Schnirelman theory, minimax theory and the theory of weighted Sobolev spaces to establish our results.