Positive solutions for some singular critical growth nonlinear elliptic equations

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