The fate of the metallic solution of the Hubbard-Holstein model
is investigated by means of Dynamical Mean-Field Theory. The paramagnetic metal
is enclosed between a Mott insulating phase, at high enough e-e interaction strength,
and a charge ordered phase at strong e-ph coupling. In the crossover region,
where the e-ph retarded interaction overcomes the e-e repulsion, a stable
s-wave SC solution is found even at half-filling. Upon doping, the SC amplitude
decreases but survives at much higer values of the e-e interaction.
The study of this simple, but not yet fully understood, model is
fundamental to elucidate the role played by optical phonons
as a pairing glue in correlated heterointerfaces, where the
electron density is very low, or in the context of cuprate superconductors.