Positive solutions of singular semilinear elliptic problems in NTA-cones

Abstract

We study the existence, the uniqueness and the asymptotic behavior of positive solutions of the nonlinear equation

in an NTA-cone in ${\mathbb{R}}^n(n\ge 3$), when a positive Borel measurable function $f(.,.)$ is continuous and non-increasing with respect to the second variable and satisfies a certain condition related to a Kato class.