  The phase diagram of a non-relativistic fermionic system with imbalanced
state populations interacting via a short-range S-wave attractive interaction
is analyzed in the mean field approximation. We determine the energetically
favored state for different values of the mismatch between the two Fermi
spheres in the weak and strong coupling regime considering both homogeneous and
non-homogeneous superconductive states. We find that the homogeneous
superconductive phase persists for values of the population imbalance that
increase with increasing coupling strength. In the strong coupling regime and
for large population differences the energetically stable homogeneous phase is
characterized by one gapless mode. We also find that the inhomogeneous
superconductive phase characterized by the condensate $\Delta({\bf x}) \sim
\Delta~\exp{(i \bf{q \cdot x})}$ is energetically favored in a range of values
of the chemical potential mismatch that shrinks to zero in the strong coupling
regime.
