AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS

Xiujuan Dong; Xue Yang

doi:10.11948/20210309

2022 Volume 12 Issue 2

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Xiujuan Dong, Xue Yang. AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 754-769. doi: 10.11948/20210309

Citation:

Xiujuan Dong, Xue Yang. AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 754-769. doi: 10.11948/20210309

AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS

Xiujuan Dong^1, ,,
Xue Yang²

1.
School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China
2.
School of Mathematics, Jilin University, Changchun 130012, China

Corresponding author: Email: dongxj391@163.com(X. Dong)

Abstract

Abstract

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.
- Affine-periodic solutions /
- perturbed systems /
- exponential dichot-omy /
- Banach contraction mapping principle
MSC: 34C25, 34C27

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