Necessary Conditions and Sufficient Conditions for Global Existence in the Nonlinear Schrödinger Equation

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 \cite{MR84d:35140,MR87i:35026}. Furthermore, we improve a blow-up condition.

Item Type: Article
Language: English
Date: 2002
Refereed: Yes
Subjects: G- MATHEMATIQUES
Divisions: Institut de mathématiques de Toulouse
Site: UT1
Date Deposited: 10 Jul 2012 15:35
Last Modified: 18 Oct 2017 15:20
URI: http://publications.ut-capitole.fr/id/eprint/6588

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