Positive solutions for some singular critical growth nonlinear elliptic equations Original Research Article

Let ΩΩ be a bounded domain in RNRN(N⩾4)(N⩾4) with smooth boundary ∂Ω∂Ω and the origin View the MathML source0∈Ω¯, μ<((N-2)/2)2μ<((N-2)/2)2, 2*=2N/(N-2)2*=2N/(N-2), K(x)K(x) is a smooth function on ΩΩ and positive somewhere. We obtain existence results of positive solutions to the Dirichlet problem View the MathML source-Δu=μu|x|2+K(x)|u|2*-2u+f(x,u) on ΩΩ, u=0u=0 on ∂Ω∂Ω for various K(x)K(x) and suitable number μμ.