带导数项的奇摄动非线性Schrdinger方程孤波解的存在性及其集中性质  

On Existence and Concentration of Solitary Waves for a Class of Singularly Perturbed Nonlinear Schrodinger Equations with Derivative Terms

作　　者：魏公明[1] 杨林林[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《数学年刊（A辑）》2013年第3期327-338,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11071164);上海市教委重点科研创新项目(No.13ZZ118)的资助

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Schrdinger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Schrdinger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.The authors study the existence and concentration of semi-classical solitary waves for a class of nonlinear SchrSdinger equations with first order derivative terms and （V）α potentials. Precisely, as the singularly perturbed parameter which corresponds to Planck constant approches to zero, the solitary waves of these nonlinear Schrodinger 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.

关 键 词：非线性SCHRODINGER方程 Lyapunov-Schmidt方法 压缩映射原理 

分 类 号：O175[理学—数学]