AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS

被引：1
|
作者：
Dong, Xiujuan [1 ]
Yang, Xue [1 ,2 ]
机构：
[1] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Sch Math & Stat, Changchun 130024, Peoples R China
[2] Jilin Univ, Sch Math, Changchun 130012, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2022年 / 12卷 / 02期
关键词：
Affine-periodic solutions; perturbed systems; exponential dichotomy; Banach contraction mapping principle; EXPONENTIAL DICHOTOMY;
D O I：
10.11948/20210309
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we try to study the existence and uniqueness of affine-periodic solutions for the perturbed affine-periodic system. We prove that, under certain conditions, if the coefficient of the forced term is sufficiently small, then the system admits affine-periodic solutions which have the form of z(t + T, mu) = Qz(t, mu) with some nonsingular matrix Q. Depending on the structure of Q, they may be periodic, anti-periodic, quasi-periodic or even unbounded spiral motions. The main tools we used are the theory of exponential dichotomy and Banach contraction mapping principle.
引用
收藏
页码：754 / 769
页数：16
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