A global compactness result for singular elliptic problems involving critical Sobolev exponent

Let Omega subset of R-N be a bounded domain such that 0 is an element of Omega, N greater than or equal to 3, 2* = 2N/N-2, lambda is an element of R, epsilon is an element of R. Let {u(n)} subset of H-0(1)(Omega) be a (P.S.) sequence of the functional E-lambda,E-epsilon(u) = 1/2 integral(Omega)(\delu\(2) - lambdau(2) / \x\(2) - epsilonu(2)) - 1/2* integral(Omega)\u\(2*). We study the limit behaviour of un and obtain a global compactness result.