arXiv:math/0511167 Abstract

arXiv:math/0511167 [math.AP]Abstract References Reviews Resources

On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent

Published 2005-11-07Version 1

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.

Categories: math.AP, math-ph, math.MP

Subjects: 35D05, 35J60, 35P30, 47H15, 58E05

Keywords: nonlinear eigenvalue problem, sobolev spaces, variable exponent, nonlinear dirichlet problems, mountain pass theorem

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