Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 220, pp. 1-13.

Title: Anisotropic problems with variable exponents and
       constant Dirichlet conditions

Authors: Maria-Magdalena Boureanu (Univ. of Craiova, Craiova, Romania)
         Cristian Udrea           (Univ. of Craiova, Craiova, Romania)
         Diana-Nicoleta Udrea     (Univ. of Craiova, Craiova, Romania)

Abstract:
 We study a general class of anisotropic problems involving
 $\vec p(\cdot)$-Laplace type operators.
 We search for weak solutions that are constant on the boundary
 by introducing a new subspace of the anisotropic Sobolev space with
 variable exponent and by proving that it is a reflexive Banach space.
 Our argumentation for the existence of weak solutions is mainly based
 on a variant of the mountain pass theorem of Ambrosetti and Rabinowitz.

Submitted April 8, 2013. Published October 04, 2013.
Math Subject Classifications: 35J25, 46E35, 35D30, 35J20.
Key Words: Anisotropic variable exponent Sobolev spaces;
           Dirichlet problem; existence of weak solutions; mountain pass theorem.