  It is proven that periodically varying and sign definite nonlinearity in a
general case does not prevent collapse in two- and three-dimensional nonlinear
Schrodinger equations: at any oscillation frequency of the nonlinearity blowing
up solutions exist. Contrary to the results known for a sign alternating
nonlinearity, increase of the frequency of oscillations accelerates collapse.
The effect is discussed from the viewpoint of scaling arguments. For the
three-dimensional case a sufficient condition for existence of collapse is
rigorously established. The results are discussed in the context of the
meanfield theory of Bose-Einstein condensates with time dependent scattering
length.
