Sign-changing solutions for elliptic problems with critical Sobolev–Hardy exponents ✩

Let Ω ⊂ RN be a smooth bounded domain such that 0 ∈ Ω, N 7, 0 s < 2, 2∗(s) = 2(N − s)/(N −2). We prove the existence of sign-changing solutions for the singular critical problem −Δu − μ(u/|x|2) = (|u|2∗(s)−2/|x|s )u + λu with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.  2003 Elsevier Inc. All rights reserved