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

Modulational Instability in Bose?Einstein Condensates under Feshbach Resonance Management