具有指数型二分性离散系统的反周期解  

Anti-periodic Solutions for Discrete Systems with Exponential Dichotomy

作　　者：孟鑫[1] MENG Xin(College of Mathematics,Jilin Normal University,Siping 136000,Jilin Province,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《吉林大学学报（理学版）》2018年第6期1423-1426,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971084);吉林省教育厅"十三五"科学技术研究规划项目(批准号:JJKH20170368KJ);吉林师范大学博士科研启动基金(批准号:吉师博2016002号)

摘　　要：考虑一类具有指数型二分性非线性离散系统的反周期解.首先证明若齐次线性系统具有指数型二分性,则对应非齐次线性系统存在反周期解;然后借助该结论及Banach不动点定理,给出非线性离散系统存在唯一反周期解的充分条件;最后给出应用实例.The author considered the anti-periodic solutions fora class of nonlinear discrete systems with exponential dichotomy.Firstly,it was proved that if the homogeneous linear system had exponential dichotomy,then the corresponding nonhomogeneous linear system had an anti-periodic solution.Secondly,by means of this conclusion and the Banach fixed point theorem,a sufficient condition for the existence and uniqueness of anti-periodic solutions fornonlinear discrete systems was given.Finally,an application example was given.

关 键 词：指数型二分性 反周期解 BANACH不动点定理 

分 类 号：O175.7[理学—数学]