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202103018.pdf
文章编号： 1672-6987（2021）03-0113-06； DOI： 10.16351/j.1672-6987.2021.03.018
张淑芳， 张新丽*（青岛科技大学 数理学院，山东 青岛 266061）
摘要： 研究了一类拟周期奇异摄动系统拟周期解的存在性和唯一性。首先，证明了与非线性项同频率的拟周期函数可以构成一个巴拿赫空间，然后利用不动点定理和拟周期函数的B-性质，证明了该奇异摄动方程响应解，即与系统同频率的拟周期解的存在性和唯一性。
关键词： 拟周期解； 奇异摄动； 非自治系统
中图分类号： O 175.1文献标志码： A
引用格式： 张淑芳， 张新丽. 一类非自治奇异摄动系统响应解的存在性［J］. 青岛科技大学学报(自然科学版), 2021, 42(3): 113-118.
ZHANG Shufang, ZHANG Xinli. Existence of response solution for a singularly perturbed nonautonomous system［J］. Journal of Qingdao University of Science and Technology（Natural Science Edition), 2021, 42(3): 113-118.
Existence of Response Solution for A Singularly Perturbed
Nonautonomous System
ZHANG Shufang, ZHANG Xinli
(College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China)
Abstract: The existence and uniqueness of quasi-periodic solutions for a quasi-periodic singularly perturbed system are investigated in this paper. First, this paper shows that all quasi-periodic functions, which have the same frequency with the nonlinear terms, form a Banach space. Then the the existence and uniqueness of response solution are obtained for the above singularly perturbed system by means of the fixed point methods and the B-property of quasi-periodic functions.
Key words: quasi-periodic solutions; singular perturbation; nonautonomous system
收稿日期： 2020-05-26
基金项目： 山东省专业学位研究生教学案例库立项建设项目(SDYAL18062).
作者简介： 张淑芳(1997—),女,硕士研究生.*通信联系人.
