Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

We study the following singular elliptic equation with critical exponent {-Delta u = Q(x)u2*(-1) + lambda u(-gamma) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, and lambda > 0, gamma is an element of (0, 1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all lambda > 0 small enough.