Positive solutions for nonparametric anisotropic singular solutions

Abstract

We consider an elliptic equation driven by a nonlinear, nonhomogeneous differential operator with nonstandard growth. The reaction has the combined effects of a singular term and of a "superlinear" perturbation. There is no parameter in the problem. Using variational tools and truncation and comparison techniques, we show the existence of at least two positive smooth solutions.

Keywords

• variable lebesgue and sobolev spaces
• anisotropic regularity
• anisotropic maximum principle
• truncations and comparisons
• hardy inequality