具有广义指数型二分性离散系统的反周期解  

Anti-Periodic Solutions for Discrete Systems with Generalized Exponential Dichotomy

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

机构地区：[1]吉林师范大学数学学院

出　　处：《西南师范大学学报（自然科学版）》2020年第1期1-5,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10971084);吉林省教育厅“十三五”科学技术项目(JJKH20170368KJ);吉林师范大学博士启动项目(吉师博2016002号)

摘　　要：研究了一类具有广义指数型二分性非线性离散系统的反周期解.首先指出若齐次线性系统具有广义指数型二分性,则对应非齐次线性系统存在反周期解.然后借助这个结论并应用不动点定理,给出了非线性离散系统存在反周期解的充分条件.In this paper,the anti-periodic solutions have been studied for nonlinear discrete systems with generalized exponential dichotomy.Firstly,it is pointed out that if the homogeneous linear system has generalized exponential dichotomy.Secondly,the nonhomogeneous linear system admits an anti-periodic solution.And lastly,by using the above conclusion and the fixed point theorem,sufficient conditions for the existence of anti-periodic solutions for nonlinear discrete systems are established.

关 键 词：广义指数型二分性 指数型二分性 反周期解 不动点定理 

分 类 号：O175.7[理学—数学]