On symmetric solutions of a singular elliptic equation with critical Sobolev–Hardy exponent

This paper is concerned with the existence of the nontrivial solutions of the following problem:{−Δu=μu|x|2+K(x)u2∗(s)−1|x|s,x∈Rn,u∈DG1,2(Rn), where n>2n>2, K(x)K(x) is a bounded, continuous function satisfying some conditions. DG1,2(Rn) is an appropriate Sobolev space of G  -symmetric functions. 2∗(s)=2(n−s)(n−2) is the critical Sobolev–Hardy exponent, and 0⩽s<20⩽s<2, 0<μ<μ¯=(n−22)2.