Existence of positive solutions to nonlinear elliptic problem in the half space

Abstract

This paper concerns nonlinear elliptic equations in the half space $mathbb{R}_{+}^{n}:={ x=(x',x_{n})in mathbb{R}^{n}:x_{n}$ greater than 0 $}$, $ngeq 2$, with a nonlinear term satisfying some conditions related to a certain Kato class of functions. We prove some existence results and asymptotic behaviour for positive solutions using a potential theory approach.

Keywords

• Green function
• elliptic equation
• positive solution.