Existence results for a class of nonhomogeneous elliptic equations with critical Sobolev exponent

In this paper we study the problem $'Delta u + u|u|2*-2+ f(x)= 0$ in $'Omega$, $u(x) = 0$ on $'partial'Omega$.Since the embedding of $H01('Omega)$ in $L2*('Omega)$ is not compact, classical variational and fixed-points approaches can not be applied to find solutions.We study that problem by making use of a fixed-point Theorem as well as one from approximation methods