  We derive the superconductiong mean-field equations for an attractive
interaction, V, in the s-wave channel when local Coulomb interactions are taken
into account for any value of U. Our results show that the Coulomb repulsion is
detrimental to the critical temperature, $T_c$, and the order parameter,
$\Delta(T)$, for values of $U \geq |V|$. Furthermore, our results depend on
band filling in a sensible way. In the presence of local correlations,
$2\Delta(0)/T_c$ differs from the BCS ratio, since Coulomb interactions affect
much more the superconducting critical temperature, $T_c$, than the
superconducting order parameter, $\Delta(T)$. We conclude that the presence of
Coulomb interactions play an additional role in the analysis of experimental
data, specially in narrow band systems.
