Positive Solutions of Nonlinear Elliptic Equations in Unbounded Domains in R 2

Abstract

We study the existence of positive solutions of the nonlinear equation Δu+f(⋅,u)=0, in D with u=0 on ∂D, where D is an unbounded domain in R2 with a compact nonempty boundary ∂D consisting of finitely many Jordan curves. The aim is to prove an existence result for the above equation in a general setting by using potential theory.