一类非自治奇异摄动系统响应解的存在性  

Existence of Response Solution for A Singularly Perturbed Nonautonomous System

作　　者：张淑芳 张新丽[1] ZHANG Shufang;ZHANG Xinli(College of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China)

机构地区：[1]青岛科技大学数理学院,山东青岛266061

出　　处：《青岛科技大学学报（自然科学版）》2021年第3期113-118,共6页Journal of Qingdao University of Science and Technology:Natural Science Edition

基　　金：山东省专业学位研究生教学案例库立项建设项目(SDYAL18062)。

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。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.

关 键 词：拟周期解 奇异摄动 非自治系统 

分 类 号：O175.1[理学—数学]