一类具有逐段常变量扰动系统的渐近概周期解  

Asymptotically Almost Periodic Solutions for a Class of Perturbed Systems with Piecewise Constant Argument

作　　者：姚慧丽[1] 张娜[1] 薛寒[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2015年第1期89-94,共6页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(12511110)

摘　　要：针对一类具有逐段常变量扰动系统的渐近概周期解的存在性问题进行了研究.具有逐段常变量的微分方程不仅是微分方程,它还具有差分方程的性质,是离散和连续的统一.利用渐近概周期函数唯一分解性质,讨论了相关差分方程的渐近概周期序列解,得到了相关方程存在唯一有界渐近概周期解的条件,然后利用指数二分法及压缩映射原理讨论了所要研究的具有逐段常变量的扰动系统渐近概周期解的存在性及唯一性.Existence of asymptotically almost periodic solutions for a class of perturbed systems with piecewise constant argument is investigated. Differential equations with piecewise constant argument are not only differential equations, they also have the nature of the difference equations, discrete and continuous unity. Using unique de- composition theorem of asymptotically almost periodic functions, XUE Han asymptotically almost periodic sequence solutions of related difference equations are discussed and the conditions of related equations with only bounded as- ymptotically almost periodic solution are obtained, then by using the exponential dichotomy and contraction mapping theory, the existence and uniqueness of asymptotically almost periodic solutions of the system is are discussed.

关 键 词：逐段常变量 扰动系统 指数二分 压缩映射原理 渐近概周期解 

分 类 号：O177.5[理学—数学]