Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation

Résumé

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