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: ⎧⎪⎨⎪ ⎩ − u = μ u |x|2 +K(x) u2∗(s)−1 |x|s , x∈ Rn, u ∈ D 1,2 G Rn , where n>2, K(x) is a bounded, continuous function satisfying some conditions. D 1,2 G (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 <2, 0<μ<μ¯ = ( n−2 2 )2. © 2006 Elsevier Inc. All rights reserved.