一类含有概周期强迫项的二阶非线性系统的概周期解  

Almost periodic solutions for a class of second-order nonlinear forced to almost periodic system

作　　者：蒋馨颖[1] 盛冠楠[1] 周贵霞[1] 

机构地区：[1]广西师范大学数学科学学院,广西桂林541004

出　　处：《贵州师范学院学报》2011年第3期5-8,共4页Journal of Guizhou Education University

摘　　要：主要研究一类含有概周期强迫项的二阶非线性系统,即二阶非线性方程x″+cx′+g(t,x)=p(t,x(t-τ))的概周期解.在参考有关文献资料的基础上,将文献[9]研究的二阶非线性方程x″+cx′+g(x)=p(t)进行适当的推广.利用文献[10]中给出的证明方程概周期解存在性的方法,即指数型二分性和压缩映射原理研究二阶时滞微分方程x″+cx′+g(t,x)=p(t,x(t-τ))概周期的存在性,得到了某些充分条件,这些条件直接与方程的系数建立联系,推广了某些已有的结果。This paper studies the existence of almost periodic solutions for a class second-order nonlinear forced to almost periodic systems.,namely,x″＋cx′＋g（t,x）=p（t,x（t-τ））.With the reference to several related documents,we study and extend properly the second-order nonlinear equation x″＋cx′＋g（t,x）=p（t,x（t-τ））by Shi Jin Lin.By using exponential dichotomies and contraction mapping principle,this paper studies the existence for almost periodic solutions and bounded solutions of second order differential equation with nonlinear forced term and gives some sufficient conditions that relate straightly with coefficients.Our work generalizes some known results in the literature.

关 键 词：指数型二分性 压缩映射原理 概周期解 有界解 不动点 二阶非线性方程 

分 类 号：O175.14[理学—数学]