Existence of solutions to nonhomogeneous Dirichlet problems with dependence on the gradient

Abstract

The goal of this article is to explore the existence of positive solutions for a nonlinear elliptic equation driven by a nonhomogeneous partial differential operator with Dirichlet boundary condition. This equation a convection term and thereaction term is not required to satisfy global growth conditions. Our approach is based on the Leray-Schauder alternative principle, truncation and comparison approaches, and nonlinear regularity theory.

Keywords

• Nonhomogeneous p-Laplacian operator
• nonlinear regularity
• Dirichlet boundary condition
• convection term
• truncation
• Leray-Schauder alternative