  Using the generalized DMFT+Sigma approach we have studied disorder influence
on single-particle properties of the normal phase and superconducting
transition temperature in attractive Hubbard model. The wide range of
attractive potentials U was studied - from the weak coupling region, where both
the instability of the normal phase and superconductivity are well described by
BCS model, towards the strong coupling region, where superconducting transition
is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at
temperatures much higher than the temperature of superconducting transition. We
have studied two typical models of conduction band with semi-elliptic and flat
densities of states, appropriate for three-dimensional and two-dimensional
systems respectively. For semi-elliptic density of states disorder influence on
all single-particle properties (e.g. density of states) is universal for
arbitrary strength of electronic correlations and disorder and is due only to
the general disorder widening of conduction band. In the case of flat density
of states universality is absent in general case, but still the disorder
influence is due mainly to band widening and universal behavior is restored for
large enough disorder. Using the combination of DMFT+Sigma and Nozieres -
Schmitt-Rink approximations we have studied disorder influence upon
superconducting transition temperature T_c for the range of characteristic
values of U and disorder, including the BCS-BEC crossover region and the limit
of strong coupling. Disorder can either suppress T_c (in the weak coupling
region) or significantly increase T_c (in strong coupling region). However in
all cases the generalized Anderson theorem is valid and all changes of
superconducting critical temperature are essentially due only to the general
disorder widening of the conduction band.
