On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent

Details On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent

2005-11-07

arxiv.org/abs/math/0511167v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a class of nonlinear Dirichlet problems involving the
$p(x)$--Laplace operator. Our framework is based on the theory of Sobolev
spaces with variable exponent and we establish the existence of a weak solution
in such a space. The proof relies on the Mountain Pass Theorem.

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