| 一类拟线性Schroedinger方程 |
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| 引用本文： | 舒级,张健,李继彬.一类拟线性Schroedinger方程[J].应用数学和力学,2007,28(7):877-882. |
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| 作者姓名： | 舒级 张健 李继彬 |
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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： | 四川省教育厅资助科研项目;致谢本得到四川师范大学校级科研基金资助,特此感谢. |
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| 摘 要： | 在二维空间中讨论一类拟线性Schroedinger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．
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| 关 键 词： | 拟线性Schroedinger方程 爆破 整体解 基态 玻色-爱因斯坦凝聚 |
| 文章编号： | 1000-0887（2007）07-0877-06 |
| 修稿时间： | 2006-09-04 |
On a Class of Quasilinear Schroedinger Equations |
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| SHU Ji, ZHANG Jian.On a Class of Quasilinear Schroedinger Equations[J].Applied Mathematics and Mechanics,2007,28(7):877-882. |
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| Authors: | SHU Ji ZHANG Jian |
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| Institution: | SHU Ji, ZHANG Jian ( 1. Sichuan Provincial Key Laboratory of Computer Software, University, Chengdu 610055, P. R. China; 2. College of Mathematics and Software Science, Siehuan Normal University, |
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| Abstract: | A type of quasilinear Schroedinger 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. |
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| Keywords: | quasilinear Schroedinger equations blow up global solution ground state Bose-Einstein condensates |
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