  We investigate the behavior of a electric potential profile inside a
mesoscopic region attached to a pair of superconducting leads. It turns out
that ${\rm I}-V$ characteristic curves are strongly modified by this profile.
In addition, the electronic population in the mesoscopic region is affected by
the profile behavior. We discuss the single particle current and the mesoscopic
electronic population within the non-equilibrium Keldysh Green functions
technique. The Keldysh technique results are further converted in a self
consistent field (SFC) problem by introducing potential profile modifications
as proposed by Datta. Evaluation of ${\rm I}-V$ characteristics are presented
for several values of the model parameters and comparison with current
experimental results are discussed.
