吉首大学学报(自然科学版)

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一类带调和势具非齐次项的非线性Schrödinger方程

SHE Zhaobing,HE Xiaofei,CHEN  Fengxia   

  1. (1.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China ;2.Zhangjiajie College,Jishou University,Zhangjiajie 427000,Hunan China)
  • 出版日期:2016-05-25 发布日期:2016-06-24
  • 通讯作者: 谌凤霞(1988—),女,湖南溆浦人,吉首大学张家界学院教师,主要从事Schr?dinger方程研究.
  • 作者简介:佘朝兵(1982—),男,湖南邵东人,吉首大学张家界学院讲师,吉首大学数学与统计学院硕士生,主要从事Schr?dinger方程研究
  • 基金资助:

    吉首大学张家界学院科研资助项目(ZYYB201605)

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

摘要:

讨论一类带调和势的具有非齐次项的非线性Schrödinger方程初值问题.通过构造对应的能量泛函、变分结构,运用势井方法、凹函数和改进过的Gagliardo-Nirenberg插值不等式,得到Cauchy问题整体解及爆破解存在的最佳条件,并且证明了整体解存在的初值具体取值范围.

关键词: 非齐次项;非线性Schrö, dinger方程;整体解;爆破解;最佳条件

Abstract:

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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