  In this paper we consider a one-dimensional non-linear Schroedinger equation
(NLSE) with a periodic potential. In the semiclassical limit we prove that the
stationary solutions of the Bose-Hubbard equation approximate the stationary
solutions of the (NLSE). In particular, in the limit of large nonlinearity
strength the stationary solutions turn out to be localized on a single lattice
site of the periodic potential; as a result the phase transition from
superfluid to Mott-insulator phase for Bose-Einstein condensates in a
one-dimensional periodic lattice is rigorously proved.
