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Matematicheskie Zametki, 2012, Volume 91, Issue 4, Pages 515–521
DOI: https://doi.org/10.4213/mzm8906 (Mi mzm8906) 		 
On a Class of Nonlinear Schrödinger Equations with Nonnegative Potentials in Two Space Dimensions

Jian Zhang, Ji Shu

Sichuan Normal University
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DOI: https://doi.org/10.4213/mzm8906
Abstract: This paper discusses a class of critical nonlinear Schrödinger equations which are closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. By constructing a constrained variational problem and considering the so-called invariant manifolds of the evolution flow, the authors derive a sharp criterion for blow-up and global existence of the solutions.
Keywords: nonlinear Schrödinger equation, global existence, blow-up, nonnegative potentials, constrained variational problem.
Received: 30.04.2010
English version:
Mathematical Notes, 2012, Volume 91, Issue 4, Pages 487–492
DOI: https://doi.org/10.1134/S0001434612030224
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Jian Zhang, Ji Shu, “On a Class of Nonlinear Schrödinger Equations with Nonnegative Potentials in Two Space Dimensions”, Mat. Zametki, 91:4 (2012), 515–521; Math. Notes, 91:4 (2012), 487–492
Citation in format AMSBIB
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