Semilinear Elliptic Equations with Singularity on the Boundary

Abstract

In this paper, we consider the existence and nonexistence of positive solutions to semilinear elliptic equation -Δu = K(x)(1-|x|)^{-λ_u^q} in the unit ball B with 0-Dirichlet boundary condition. Our main tools are based on the interior estimates of the Schauder type, the Schauder fixed point theorem and the pointwise estimates for Green functions.