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Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation
Bégout, Pascal
HAL, hal-00715805 / Harvested from HAL
Text on HAL
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.
Publié le : 2002-07-05
Classification:  2000 Mathematics Subject Classification: 35Q55,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00715805,
     author = {B\'egout, Pascal},
     title = {Necessary conditions and sufficient conditions for global existence in the nonlinear Schr\"odinger equation},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00715805}
}

Bégout, Pascal. Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00715805/