Existence of sign-changing solutions for semilinear singular elliptic equations with critical Sobolev exponents

We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N⩾4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively.