A GENERAL AVERAGING METHOD FOR AFFINE PERIODIC SOLUTIONS

作     者：Xue YANG Jiamin XING Yong LI 杨雪;邢佳敏;李勇

作者机构：College of MathematicsJilin UniversityChangchun 130012China School of Mathematics and Statisticsand Center for Mathematics and Interdisciplinary Sci Northeast Normal UniversityChangchun 130024China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2024年第44卷第6期

页      面：2207-2224页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(12371191 12071175) supported by the NSFC(12071175 11901080) supported by the NSFC(12071175) the Fundamental Research Funds For the Central Universities(2412023YQ003) the Natural Science Foundation of Jilin Province(20200201253JC) 

主　　题：affine-periodic solution perturbed system Brouwer degree averaging method 

摘      要：We consider the persistence of affine periodic solutions for perturbed affine periodic ***(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T0 is fixed and Q is a nonsingular *** are a kind of spatiotemporal symmetric solutions,*** *** give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system s affine periodic *** transversal condition is determined using the Brouwer *** also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.