Nontrivial solutions for some singular critical growth semilinear elliptic equations Original Research Article

Let ΩΩ be a bounded domain in View the MathML sourceRN(N≥5) with smooth boundary ∂Ω∂Ω and the origin View the MathML source0∈Ω,μ<μ̄=((N−2)/2)2,2∗=2N/(N−2),K(x) is a bounded positive function on View the MathML sourceΩ̄. We prove the existence results for nontrivial solutions to the Dirichlet problem View the MathML source−△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.