  This work is devoted to the Dirichlet problem for the equation (-\Delta u =
\lambda u + |x|^\alpha |u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$.
  We assume that $\lambda$ is bigger than the first eigenvalues of the
laplacian, and we prove that there exists a solution provided $\alpha$ is small
enough. This solution has a variational characterization as a ground state.
