Multiple solutions for a boundary singular semilinear equation with sublinear term involving Hardy potential and Hardy-Sobolev exponent

In this paper we establish the existence of at least two solutions to a singular elliptic equations 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 its depends of sign of the mass of the domain.