Existence results for singular critical elliptic problems in RN ✩

In the paper we consider the following semilinear elliptic problems with critical Sobolev–Hardy exponents: ⎧⎪ ⎨⎪ ⎩ − u − μ |x|2 u+ λV (x)u = K(x) |u|2∗(s)−2 |x|s u, in RN, lim |x|→∞ u(x) = 0, (Pμ,s ) where N 3, 0 μ < μ¯ := (N−2 2 )2, λ > 0, 0 s < 2, 2∗(s) = 2(N−s) N−2 . Under suitable conditions, we prove that (Pμ,s) has at least one nontrivial solution by means of Linking theorem. Also via the Pseudo-index theory, we consider the multiplicity of nontrivial solutions for (Pμ,s ). © 2007 Elsevier Inc. All rights reserved.