Solutions for semilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy potential

Let Ω⊂RN be a smooth bounded domain such that 0∈Ω, N≥5, 0≤s<2, 2∗(s)=2(N−s)N−2. We prove the existence of nontrivial solutions for the singular critical problem −Δu−μu|x|2=|u|2∗(s)−2|x|su+λu with Dirichlet boundary condition on Ω for all λ>0 and 0≤μ<(N−22)2−(N+2N)2.