| 一类具非线性二阶导数项的Schrōdinger方程整体解存在的最佳条件 |
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| 引用本文： | 舒级,张健.一类具非线性二阶导数项的Schrōdinger方程整体解存在的最佳条件[J].应用数学学报,2007,30(3):462-467. |
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| 作者姓名： | 舒级 张健 |
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| 作者单位： | [1]四川师范大学计算机软件实验室,成都610066 [2]四川师范大学数学与软件科学学院,成都610066 |
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| 基金项目： | 国家自然科学基金（10271084）,教育部优秀青年教师资助计划项目（教人司[2003]355号）,四川省教育厅资助科研项目和四川师范大学科研项目资助项目.致谢作者感谢审稿人的有益建议. |
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| 摘 要： | 本文讨论一类具非线性二阶导数项的Schrodinger方程,它在物理上描述了上混合振荡传播．根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在．
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| 关 键 词： | 具非线性二阶导数项的Schrōdinger方程 最佳条件 整体解 爆破 基态 |
| 修稿时间： | 2005-12-142006-09-11 |
Sharp Condition of Global Existence for a Class of Second Order Derivative Nonlinear Schroedinger Equations |
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| SHU Ji, ZHANG JIAN.Sharp Condition of Global Existence for a Class of Second Order Derivative Nonlinear Schroedinger Equations[J].Acta Mathematicae Applicatae Sinica,2007,30(3):462-467. |
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| Authors: | SHU Ji ZHANG JIAN |
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| Institution: | Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu 610066;College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066 |
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| Abstract: | This paper discusses a type of second order derivative nonlinear SchrSdinger equations which are used to describe the upper-hybrid oscillation propagation in physics. In terms of the variational characteristics of the ground state, by applying the potential well argument and the concavity method, we get a sharp condition for global existence to the solutions of this equation. In addition, that how small the initial are, the global solutions exist is also given. |
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| Keywords: | second order derivative nonlinear SchrSdinger equation sharp condition global solution blow-up ground state |
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