  Superconductivity in strongly correlated systems is a remarkable phenomenon
that attracts a huge interest. The study of this problem is relevant for
materials as the high Tc oxides, pnictides and heavy fermions. In this work we
study a realistic model that includes the relevant physics of superconductivity
in the presence of strong Coulomb correlations. We consider a two-band model,
since most of these correlated systems have electrons from at least two
different atomic orbitals coexisting at their Fermi surface. The Coulomb
repulsion is taken into account through a local repulsive interaction. Pairing
is considered among quasi- particles in neighbouring sites and we allow for
different symmetries of the order parameter. In order to deal with the strong
local correlations, we use the well known slave boson approach that has proved
very successful for this problem. Here we are interested in obtaining the zero
temperature properties of the model, specifically its phase diagram and the
existence and nature of superconducting quantum critical points. We show that
these can arise by increasing the mixing between the two bands. Since this can
be controlled by external pressure or doping, our results have a direct
relation with experiments. We show that the superconductor-to-normal transition
can be either to a metal, a correlated metal or to an insulator. Also we
compare the relative stability of s and d-wave paired states for different
regions of parameter space and investigate the BCS- BEC crossover in the
two-band lattice model as function of the strength of the pairing interaction.
