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Sharp criterion of global existence for nonlinear Schrödinger equation with a harmonic potential

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Abstract

This paper discusses nonlinear Schrödinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions.

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Authors and Affiliations

  1. Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu, 610066, P. R. China

    Ji Shu

  2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P. R. China

    Ji Shu & Jian Zhang

Authors
  1. Ji Shu
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  2. Jian Zhang
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Correspondence to Ji Shu.

Additional information

Supported by the National Natural Science Foundation of China (No. 10747148, No. 10771151) and the Scientific Research Fund of Sichuan Provincial Education Department (08ZA041)

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Shu, J., Zhang, J. Sharp criterion of global existence for nonlinear Schrödinger equation with a harmonic potential. Acta. Math. Sin.-English Ser. 25, 537–544 (2009). https://doi.org/10.1007/s10114-009-7473-4

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  • DOI: https://doi.org/10.1007/s10114-009-7473-4

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