  In the present short communication, we revisit nonlinearity management of the
time-periodic nonlinear Schrodinger equation and the related averaging
procedure. We prove that the averaged nonlinear Schrodinger equation does not
support the blow-up of solutions in higher dimensions, independently of the
strength in the nonlinearity coefficient variance. This conclusion agrees with
earlier works in the case of strong nonlinearity management but contradicts
those in the case of weak nonlinearity management. The apparent discrepancy is
explained by the divergence of the averaging procedure in the limit of weak
nonlinearity management.
