一类周期离散非线性薛定谔系统的驻波解  

Standing Wave Solutions for Periodic Discrete Nonlinear Schrodinger Systems

作　　者：买阿丽[1,2] 孙国伟[1] 张凤琴[1] 

机构地区：[1]运城学院应用数学系,运城044000 [2]广州大学数学与信息科学学院,广州510006

出　　处：《应用数学学报》2014年第1期22-30,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11071283);生物数学重点实验室开放课题(SWSX201302)资助项目

摘　　要：本文考虑了一类周期离散非线性薛定谔系统,在一个比经典Ambrosetti-Rabinowitz条件更弱的超线性条件下,利用Szulkin和Weth介绍的广义Nehari流形方法,证明了该类系统驻波解的存在性,推广了已有的相关结论.类似的方法可以用来研究单个的离散薛定谔方程解的存在性.In this paper, we consider a class of periodic discrete nonlinear Schr6dinger systems. Under a weaker superlinear condition than the classical Ambrosetti-Rabinowitz condition, by using the generalized Nehari manifold approach developed by Szulkin and Weth, we prove the existence of standing wave solutions for discrete SchrSdinger systems, the results generalize the corresponding work of known literature. The same method can also be applied to obtain solutions for single discrete nonlinear Schr6dinger equation.

关 键 词：临界点理论 驻波解 广义Nehari流形 基态解 

分 类 号：O175.1[理学—数学]