Multiplicity of solutions for a nonlinear degenerate problem in anisotropic variable exponent spaces

We study a nonlinear elliptic problem with Dirichlet boundary condition involving an anisotropic operator with variable exponents on a smooth bounded domain ??RN. For that equation we prove the existence of at least two nonnegative and nontrivial weak solutions. Our main result is proved using as main tools the Mountain Pass Theorem and a direct method in Calculus of Variation.