Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain

Abstract

" We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation \u0394u-Vu=g(\u22c5,u), where V and g are Borel measurable functions, required to satisfy suitable assumptions related to a new functional class J. Our approach uses the Schauder fixed point theorem."