| 带导数项的奇摄动非线性 Schrodinger方程孤波解的存在性及其集中性质 |
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| 引用本文： | 魏公明,杨林林.带导数项的奇摄动非线性 Schrodinger方程孤波解的存在性及其集中性质[J].数学年刊A辑(中文版),2013,34(3):327-338. |
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| 作者姓名： | 魏公明 杨林林 |
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| 作者单位： | 上海理工大学理学院, 上海 200093.;上海理工大学理学院, 上海 200093. |
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| 基金项目： | 国家自然科学基金 (No.11071164)和上海市教委重点科研创新项目(No.13ZZ118) |
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| 摘 要： | 利用Lyapunov-Schmidt方法证明了带有一阶导数项和(V)α势函数的非线性Schrodinger方程半经典孤波解的存在性及其集中性质.
具体地讲,当相当于Planck常数的奇摄动参数趋于零时,证明了该非线性Schrodinger方程的孤波解存在并且这些解在其势函数的非退化临界点处集中.
研究的是椭圆型方程的奇摄动问题,方程带有一阶导数项是本文特征之一.
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| 关 键 词： | 非线性Schrodinger方程 Lyapunov-Schmidt方法 压缩映射原理 |
On Existence and Concentration of Solitary Waves for a
Class of Singularly Perturbed Nonlinear Schrodinger
Equations with Derivative Terms |
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| WEI Gongming and YANG Linlin.On Existence and Concentration of Solitary Waves for a
Class of Singularly Perturbed Nonlinear Schrodinger
Equations with Derivative Terms[J].Chinese Annals of Mathematics,2013,34(3):327-338. |
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| Authors: | WEI Gongming and YANG Linlin |
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| Institution: | College of Science, University of Shanghai for Science and Technology,
Shanghai 200093, China.;College of Science, University of Shanghai for Science and Technology,
Shanghai 200093, China. |
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| Abstract: | The authors study the existence and concentration of semi-classical solitary waves
for a class of nonlinear Schr¨odinger equations with first order derivative terms and (V )
potentials. Precisely, as the singularly perturbed parameter which corresponds to Planck
constant approches to zero, the solitary waves of these nonlinear Schr¨odinger equations
concentrate at the non-degenerate critical points of potentials. The authors concern singular
perturbation of semilinear elliptic equations with first order derivative terms and this is also
a new feature of the paper. |
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| Keywords: | Nonlinear Schrodinger equation Lyapunov-Schmidt method Contraction mapping principle |
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