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

T.-L. Dinu

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 208-217.

Résumé

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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