| 带斯塔克势的非线性Schroedinger方程L^2集中性质 |
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| 引用本文： | 张小云.带斯塔克势的非线性Schroedinger方程L^2集中性质[J].四川师范大学学报(自然科学版),2006,29(6):652-654. |
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| 作者姓名： | 张小云 |
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| 作者单位： | 四川师范大学数学与软件科学学院,四川成都610066 |
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| 基金项目： | 四川省青年基金和四川省教育厅自然科学重点基金资助项目 |
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| 摘 要： | 讨论了带斯塔克势的非线性Schroedinger方程爆破解的定性性质，运用一个变量替换建立了带斯塔克势的非线性Schroedinger方程与不带势的经典非线性Schroedinger方程之间的联系．结合经典非线性Schroedinger方程的性质，进一步研究了临界的带斯塔克势的非线性Schroedinger方程爆破解的结构，证明了其爆破解具有L^2集中性质．特别地，当初始值条件径向对称时，证明了原点O为集中点．
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| 关 键 词： | 非线性Schrioedinger方程 斯塔克势 爆破解 L^2集中性质 |
| 文章编号： | 1001-8395（2006）06-0652-03 |
| 收稿时间： | 2005-11-29 |
| 修稿时间： | 2005年11月29 |
L^2 -concentration Properties for Nonlinear Schroedinger Equation with Stark Potential |
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| ZHANG Xiao-yun.L^2 -concentration Properties for Nonlinear Schroedinger Equation with Stark Potential[J].Journal of Sichuan Normal University(Natural Science),2006,29(6):652-654. |
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| Authors: | ZHANG Xiao-yun |
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| Institution: | College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan |
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| Abstract: | We study the qualitative property of critical nonlinear Schroedinger equation with Stark potential, using a transformation of variables, we establish the relation between the nonlinear Schroedinger equations with and without Stark potential. Combined with the properties of the nonlinear Schroedinger equation without potential, we study the structure of the blow-up solutions of the critical Schoedinger equation with a Stark potential, we prove that the blow-up solutions have center L^2-concentration property. Especially, if the initial data is radially symmetric, the origin is the concentration point. |
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| Keywords: | Nonlinear Schoedinger equation Stark potential Blow-up solution L^2 -concentration properties |
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