Multiple positive solutions for singular elliptic equations with weighted Hardy terms and critical Sobolev-Hardy exponents

Variational methods are used to prove the multiplicity of positive solutions for the following singular elliptic equation: -Delta u - mu/vertical bar x vertical bar(2)u = lambda f(x)vertical bar u vertical bar(q-2) + g(x)vertical bar u vertical bar(2*(s)-2)/vertical bar x vertical bar(s)u in Omega, u = 0 on partial derivative Omega, where 0 epsilon Omega subset of R(N) , N >= 3, is a bounded domain with smooth boundary partial derivative Omega, lambda > 0, 1 <= q < 2, 0 <= mu < (mu) over bar = (N - 2)(2)/4, 0 <= s < 2, 2*(s) = 2(N - s) and f and g are continuous functions on Omega, that change sign on Omega.