Nontrivial solutions for some singular critical growth semilinear elliptic equations

Let ΩΩ be a bounded domain in RN(N≥5) with smooth boundary ∂Ω∂Ω and the origin 0∈Ω,μ<μ̄=((N−2)/2)2,2∗=2N/(N−2),K(x) is a bounded positive function on Ω̄. We prove the existence results for nontrivial solutions to the Dirichlet problem −△u=μu|x|2+K(x)|u|2∗−2+λu in Ω,u=0Ω,u=0 on ∂Ω∂Ω, for suitable numbers μμ and λλ.