Journal of Jishou University(Natural Sciences Edition)

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Inhomogeneous Nonlinear Schrdinger Equation with Harmonic Potential

(1.吉首大学数学与统计学院,湖南 吉首416000;2.吉首大学张家界学院,湖南 张家界 427000)   

  1. (1.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China ;2.Zhangjiajie College,Jishou University,Zhangjiajie 427000,Hunan China)
  • Online:2016-05-25 Published:2016-06-24


The inhomogeneous nonlinear Schrödinger equation with harmonic potential is discussed.By establishing the corresponding energy function and the variational structure and through applying the potential well argument,the concave function and the improved Gagliardo-Nirenberg interpolation inequation,the optimum conditions for the global solution and explosive solution for the Cauchy problem are obtained.In addition,the initial value for the existence of global solution is determined.

Key words: inhomogeneous, nonlinear Schrö, dinger equation, global solution, explosive solution, optimum conditions

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