A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

We study the boundary value problem -div(a(x, del u)) = lambda(mu(gamma-1)-mu(beta-1)) in ohm u=0 on partial derivative ohm, where ohm is a smooth bounded domain in R-N and div(a(x, del u)) is a p(x)-Laplace type operator, with 1 < beta < gamma < inf(x is an element of ohm)p(x). We prove that if is large enough then there exist at least two non-negative weak solutions. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.