Positive solution for a boundary singular semilinear equation with Hardy–Sobolev exponent

Abstract

ABSTRACT In this paper, we establish the existence of at least one positive solution to a singular elliptic equation with zero boundary data and critical Hardy–Sobolev exponent. We show that the existence of the positive solution in high dimension depends on the sign of the mean curvature of the boundary near zero and in the low dimensions, it depends on the mass of the domain.