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

Abstract

Let Ω⊂ R N 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.