一类拟线性Schrödinger方程

舒级; 张健

一类拟线性Schrödinger方程

舒级^1,2,
张健²

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

基金项目: 四川省教育厅资助科研项目

详细信息

作者简介:
舒级(1977- ),男,四川纳溪人,讲师,博士(联系人.Tel:+86-28-84761502;E-mail:shu.ji@163.com;shuji2008@hotmail.com).

中图分类号: O175.27
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- 被引次数: 0
出版历程
- 收稿日期: 2006-09-04
- 修回日期: 2007-04-27
- 刊出日期: 2007-07-15

On a Class of Quasilinear Schr^Ldinger Equations

SHU Ji^1,2,
ZHANG Jian²

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

摘要

摘要: 在二维空间中讨论一类拟线性Schrdinger方程,该方程在物理学上描述了吸引玻色-爱因斯坦凝聚．通过建立这个方程的性质,运用能量方法,证明了该方程所对应的初值问题的解在一定条件下爆破．同时利用变分方法，也得到了整体解存在的一个充分条件,该条件与一个经典的椭圆方程的基态有关．
- 拟线性Schrdinger方程 /
- 爆破 /
- 整体解 /
- 基态 /
- 玻色-爱因斯坦凝聚
Abstract: A type of quasilinear Schr^Ldinger equations in two dimensions are discussed, which describe attractive Bose-Einstein Condensates in physics. By establishing the property of the equation and applying the energymethod, was proved the blowup of the solutions to the Cauchy problem for the equation under certain conditions. At the same time, by the variational method, the a sufficient condition of global existence was got, which is related to the ground state of a classical elliptic equation.
- quasilinear Schr^Ldinger equations /
- blow up /
- global solution /
- ground state /
- Bose-Einstein condensates

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参考文献(22)

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