Positive Solutions of singular semilinear elliptic equation in bounded NTA- Domains

Abstract

We study the existence, the uniqueness and the sharp estimate of a positive solution of the nonlinear equation $$ \Delta v +\psi(.,v)=0,$$ in a bounded NTA-domain $\Omega$ in $\mathbb{R}^n \; (n\geq 2)$, when a measurable function $\psi(.,.)$ is continuous and non-increasing with respect to the second variable.