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

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

2006-07-21

arxiv.org/abs/math/0607553v1

Mathematics

Analysis of PDEs

Proceedings A of the Royal Society of London, in press

Scientific paper

10.1098/rspa.2005.1633

We study a Dirichlet boundary value problem associated to an anisotropic differential operator on a smooth bounded of $\Bbb R^N$. Our main result establishes the existence of at least two different non-negative solutions, provided a certain parameter lies in a certain range. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of Mountain Pass lemma.

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