  We investigate the possibility of multi-band superconductivity in SrTiO$_{3}$
films and interfaces using a two-dimensional two-band model. In the undoped
compound, one of the bands is occupied whereas the other is empty. As the
chemical potential shifts due to doping by negative charge carriers or
application of an electric field, the second band becomes occupied, giving rise
to a strong enhancement of the transition temperature and a sharp feature in
the gap functions, which is manifested in the local density of states spectrum.
By comparing our results with tunneling experiments in Nb-doped SrTiO$_{3}$, we
find that intra-band pairing dominates over inter-band pairing, unlike other
known multi-band superconductors. Given the similarities with the value of the
transition temperature and with the band structure of LaAlO$_{3}$/SrTiO$_{3}$
heterostructures, we speculate that the superconductivity observed in
SrTiO$_{3}$ interfaces may be similar in nature to that of bulk SrTiO$_{3}$,
involving multiple bands with distinct electronic occupations.
