Solutions for semilinear elliptic problems with critical Sobolev–Hardy exponents and Hardy potential Original Research Article

Let Ω⊂RNΩ⊂RN be a smooth bounded domain such that 0∈Ω0∈Ω, N≥5N≥5, 0≤s<20≤s<2, View the MathML source2∗(s)=2(N−s)N−2. We prove the existence of nontrivial solutions for the singular critical problem View the MathML source−Δu−μu|x|2=|u|2∗(s)−2|x|su+λu with Dirichlet boundary condition on ΩΩ for all λ>0λ>0 and View the MathML source0≤μ<(N−22)2−(N+2N)2.