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Communications in Partial Differential Equations Volume 30, 2005 - Issue 10
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Original Articles

Sharp Threshold for Blowup and Global Existence in Nonlinear Schrödinger Equations Under a Harmonic Potential

Jian Zhang Department of Mathematics, Sichuan Normal University, Chengdu, ChinaCorrespondence[email protected]
Pages 1429-1443 | Received 01 Mar 2004, Accepted 03 Apr 2004, Published online: 14 Feb 2007
 
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ABSTRACT

We present a variational approach to study the nonlinear Schrödinger equations under a harmonic potential. By constructing a type of cross constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we derive a sharp threshold for global existence and blowup of the solution. The stability of the standing waves is also discussed.

Mathematics Subject Classification (2000):

Acknowledgments

I am grateful to Professor Y. Tsutsumi for his helpful comments, and to Professor M. Ohta for valuable discussions. Supported by the National Science Foundation of China (Project No. 10271084).

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