  The phase diagram of the attractive Hubbard model with spatially
inhomogeneous interactions is obtained using a single site dynamical mean field
theory like approach. The model is characterized by three parameters: the
interaction strength, the active fraction (fraction of sites with the
attractive interaction), and electron filling. The calculations indicate that
in a parameter regime with intermediate values of interaction strength
(compared to the bare bandwidth of the electrons), and intermediate values of
the active fraction, "non-BCS" superconductivity is obtained. The results of
this work are likely to be relevant to many systems with spatially
inhomogeneous superconductivity such as strongly correlated oxides, systems
with negative U centers, and, in future, cold atom optical lattices.
