| 带有导数项非线性Schrodinger方程行波解的存在性 |
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| 引用本文： | 杨林林,孙宗玉,魏公明. 带有导数项非线性Schrodinger方程行波解的存在性[J]. 上海理工大学学报, 2012, 34(6) |
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| 作者姓名： | 杨林林 孙宗玉 魏公明 |
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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;上海理工大学 理学院,上海200093 |
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| 摘 要： | 研究了一类带有一阶导数摄动项的非线性Schrodinger方程行波解的性质,利用Lyapunov-Schmidt方法及压缩映射原理,证明了非线性Schrodinger方程行波解的存在性和集中性质,即相当于Planck常数的摄动参数趋于零时,证明了该非线性Schrodinger方程的行波解的存在性,且这些解集中在其势函数的非退化临界点处.
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| 关 键 词： | 非线性Schrodinger方程 Lyapunov-Schmidt方法 压缩映射 |
Existence of Standing Waves for a Class of Nonlinear Schrodinger Equations with Derivative Terms |
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| YANG Lin lin,SUN Zong yu and WEI Gong ming. Existence of Standing Waves for a Class of Nonlinear Schrodinger Equations with Derivative Terms[J]. Journal of University of Shanghai For Science and Technology, 2012, 34(6) |
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| Authors: | YANG Lin lin SUN Zong yu WEI Gong ming |
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| Abstract: | The existence and concentration of standing waves were studied for a class of nonlinear Schrodinger equations with first order derivative terms.Preci-sely,as the small parameter(which corresponds to Planck constant) approches to zero,the standing waves of these nonlinear Schrodinger equations concentrate at the non degenerate critical points of potentials.The paper concerns the singular perturbation of elliptic equations with first order derivative terms and this is also a new feature of the paper. |
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| Keywords: | nonlinear Schrodinger equations Lyapunov-Schmidt method contraction mapping |
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