Nontrivial solutions for some singular critical growth semilinear elliptic equations

Let Omega be a bounded domain in R-N (N >= 5) with smooth boundary partial derivative Omega and the origin 0 epsilon Omega, mu < <(mu)over bar> = ((N - 2)/2)(2), 2* = 2N/(N - 2), K(x) is a bounded positive function on (Omega) over bar. We prove the existence results for nontrivial solutions to the Dirichlet problem -Delta u = mu u/ |x|(2) + K(x)|u|2*-2 + lambda u in Omega, u = 0 on delta Omega, for suitable numbers mu and lambda. (C) 2007 Elsevier Ltd. All rights reserved.