Existence results for nonlinear elliptic equations in bounded domains of $R^n$

Abstract

We establish existence results for the boundary-value problem $Delta u+f(.,u)=0$ in a smooth bounded domain in $mathbb{R}^n$ $(ngeq 2)$, where $f$ satisfies some appropriate conditions related to a Kato class. The proofs are based on various techniques related to potential theory.

Keywords

• Green function
• elliptic equation
• positive solutions.