Bégout, Pascal (2002) Necessary Conditions and Sufficient Conditions for Global Existence in the Nonlinear Schrödinger Equation. Advances in mathematical sciences and applications, 12 (2). pp. 817-827.

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Abstract

In this paper, we consider the nonlinear Schrödinger equation with the super critical power of nonlinearity in the attractive case. We give a sufficient condition and a necessary condition to obtain global or blowing up solutions. These conditions coincide in the critical case, thereby extending the results of Weinstein [26,27]. Furthermore, we improve a blow-up condition.