Volume 36 • Number 1 • 2013   • Multiplicity of Solutions for a Nonlinear Degenerate Problem in Anisotropic Variable Exponent Spaces Denisa Stancu-Dumitru Abstract. We study a nonlinear elliptic problem with Dirichlet boundary condition involving an anisotropic operator with variable exponents on a smooth bounded domain $\Omega\subset \mathbb R^N$. 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. 2010 Mathematics Subject Classification: 35J60, 35J70, 46E30 Full text: PDF