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In this paper, we consider the nonlinear Schr\"odinger equation with thesuper critical power of nonlinearity in the attractive case. We give asufficient condition and a necessary condition to obtain global or blowing upsolutions. These conditions coincide in the critical case, thereby extendingthe results of Weinstein. Furthermore, we improve a blow-up condition.

Necessary conditions and sufficient conditions for global existence in the nonlinear Schr\"odinger equation