具有非线性阻尼项和周期强迫项的次线性不对称可逆系统的拟周期解  

Quasiperiodic solutions for sublinear asymmetric reversible systems with a nonlinear damping and periodic forcing term

作　　者：汪小明[1,2] WANG XiaoMing

机构地区：[1]上饶师范学院数学与计算机科学学院,上饶334001 [2]南开大学陈省身数学研究所,天津300071

出　　处：《中国科学：数学》2016年第11期1703-1714,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11461056)资助项目

摘　　要：本文考虑一类具有非线性阻尼项和周期强迫项的次线性不对称可逆系统x′′+α(x^+)^(1/3)-β(x^-)^(1/3)+q(x)g(x′)+f(x)=e(t)的Aubry-Mather集和拟周期解的存在性,其中x~±=max{±x,0},q(x)、g(x)和f(x)均是R上连续可微函数,e(t)是R上连续2π-周期函数.利用周修义(Shuinee Chow)和裴明亮建立的可逆系统的Aubry-Mather定理,在函数q(x)、f(x)和e(t)具有某种奇偶性假设条件下,本文证明了该可逆系统存在无穷多广义拟周期解.In this paper, we investigate the existence of Aubry-Mather sets and quasi-periodic solutions for the sublinear asymmetric oscillator with a nonlinear damping and periodic forcing term x″＋a（x＋）1/3-β（x-）1/3＋q（x）g（x′）＋f（x）=et,where x ±=max{±x,0} q, g and f belong to the class C1 （ ）, and e is a continuous 27r-periodic function. Under some assumptions on the parities of q, f and e, we prove that there are infinitely many generalized quasi-periodic solutions by a result of Shuinee Chow and Mingliang Pei for Aubry-Mather theory theorem of reversible mapping.

关 键 词：可逆系统 次线性 不对称 拟周期解 Aubry—Mather集 

分 类 号：O175[理学—数学]