带有导数项非线性Schrdinger方程行波解的存在性  

Existence of Standing Waves for a Class of Nonlinear Schrdinger Equations with Derivative Terms

作　　者：杨林林[1] 孙宗玉[1] 魏公明[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2012年第6期593-597,共5页Journal of University of Shanghai For Science and Technology

摘　　要：研究了一类带有一阶导数摄动项的非线性Schrdinger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Schrdinger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Schrdinger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.The existence and concentration of standing waves were studied for a class of nonlinear Schr6dinger 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 Schr6dinger 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.

关 键 词：非线性Schrdinger方程 Lyapunov-Schmidt方法 压缩映射 

分 类 号：O175.2[理学—数学]