一类带有两个扰动微分方程的渐近概周期解  

Asymptotically Almost Periodic Solutions for a Class of Differential Equations with Two Perturbations

作　　者：姚慧丽 孙源源 王晶囡 张娜 YAO Hui-li;SUN Yuan-yuan;WANG Jing-nan;ZHANG Na(School of Sciences, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]哈尔滨理工大学理学院数学系,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2020年第2期138-145,共8页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金青年基金(11801122)。

摘　　要：在众多研究中,很多现象都是用微分方程作为数学模型的。但在建立方程的过程中,不可避免地会出现一些干扰力,这类方程称为带扰动的微分方程。利用压缩映像原理以及指数二分的相关结论,对一类带有两个较小的正扰动的微分方程的渐近概周期解给于讨论,给出了这类方程存在唯一的渐近概周期解的条件。Differential equations are used as mathematical models for many phenomena in numerous studies.Some interference will inevitably appear in the process of establishing equations,this kind of equations are called differential equations with perturbations.Asymptotically almost periodic solutions for a class of differential equations with two smaller positive perturbations are discussed using related theories of the principle of compressed image and exponential dichotomy,the conditions which make this kind equation have unique asymptotically almost periodic solutions are given in this paper.

关 键 词：渐近概周期解 扰动 微分方程 压缩映像原理 指数二分 

分 类 号：O175[理学—数学]