Existence results for some anisotropic Dirichlet problems

This paper concerns with a class of elliptic anisotropic Dirichlet problems depending of one real parameter on bounded Euclidean domains. Our approach is based on variational and topological methods. More concretely, along the paper we show the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci and Serrin theorem in addition to a local minimum result for differentiable functionals due to Ricceri. This abstract approach has been developed for equations on Carnot groups; see [15].