Existence results for singular critical elliptic problems in RNRN

In the paper we consider the following semilinear elliptic problems with critical Sobolev–Hardy exponents:equation(Pμ,sPμ,s){−Δu−μ|x|2u+λV(x)u=K(x)|u|2∗(s)−2|x|su,inRN,lim|x|→∞u(x)=0, where N⩾3N⩾3, 0⩽μ<μ¯:=(N−22)2, λ>0λ>0, 0⩽s<20⩽s<2, 2∗(s)=2(N−s)N−2. Under suitable conditions, we prove that (Pμ,sPμ,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,sPμ,s).