New multiple positive solutions for elliptic equations with singularity and critical growth

In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation -Delta u = lambda/u gamma + u(2*-1), x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega is a smooth bounded domain in R-N (N >= 3), 2* = 2N/N-2, gamma is an element of(0, 1) and lambda > 0 is a real parameter. We show by the variational methods and perturbation functional that the problem has at least two positive solutions w(0)(x) and w(1)(x) with w(0)(x) < w(1)(x) in Omega.