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

Abstract

This paper concerns nonlinear elliptic equations in the half space ℝn+ := {x = (x' , xn) ∈ ℝn : xn > 0}, n ≥ 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.