A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
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- 31 March 2006
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 462 (2073) , 2625-2641
- https://doi.org/10.1098/rspa.2005.1633
Abstract
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.Keywords
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