  We investigate the modulational instability of nonlinear Schr{\"o}dinger
equations with periodic variation of their coefficients. In particular, we
focus on the case of the recently proposed, experimentally realizable protocol
of Feshbach Resonance Management for Bose-Einstein condensates. We derive the
corresponding linear stability equation analytically and we show that it can be
reduced to a Kronig-Penney model, which allows the determination of the windows
of instability. The results are tested numerically in the absence, as well as
in the presence of the magnetic trapping potential.
