Singular elliptic problems with lack of compactness

We consider the following nonlinear singular elliptic equation -div (\x\(-2a)del u) = K(x)\x\(-bp)\u\(p-2)u + lambda g(x) in R-N, where g belongs to an appropriate weighted Sobolev space and p denotes the Caffarelli-Kohn-Nirenberg critical exponent associated to a, b, and N. Under some natural assumptions on the positive potential K(x) we establish the existence of some lambda(o) > 0 such that the above problem has at least two distinct solutions provided that lambda is an element of (0, lambda(o)). The proof relies on Ekeland's variational principle and on the mountain pass theorem without the Palais-Smale condition, combined with a weighted variant of the Brezis-Lieb lemma.