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

We study the boundary value problem in , u =0 on , where is a smooth bounded domain in and is a -Laplace type operator, with . We prove that if λ 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.