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We study a Dirichlet boundary value problem associated to an anisotropicdifferential operator on a smooth bounded of $\Bbb R^N$. Our main resultestablishes the existence of at least two different non-negative solutions,provided a certain parameter lies in a certain range. Our approach relies onthe variable exponent theory of generalized Lebesgue-Sobolev spaces, combinedwith adequate variational methods and a variant of Mountain Pass lemma.Comment: Proceedings A of the Royal Society of London, in pres

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