一类无穷时滞脉冲微分积分方程的概周期解  

Existence and Uniqueness of Almost Periodic Solutions to the Class of Integro-differential Equation with Impulses and Infinite Delays

作　　者：林远华[1] 冯春华[2] 

机构地区：[1]河池学院数学系,广西宜州546300 [2]广西师范大学数学科学学院,广西桂林541004

出　　处：《梧州学院学报》2009年第3期1-9,共9页Journal of Wuzhou University

基　　金：广西教育厅科研基金资助项目(200708LX163);河池学院科研项目资助课题(2008A-N001);河池学院应用数学重点学科资助项目(院科研[2007]2号)

摘　　要：研究一类高维无穷时滞的非线性脉冲微分积分方程x'(t)=A(t,x(t))x(t)+integral from n=-∞(C(t,s)g(s,x(s)ds))+sum from i=1 to m(fi(t,x(t-ti)))+b(t),t≠tk,Δx(t)=Bkx(t)+Ik(x(t))+rk,t=tk,k∈Z.概周期解的存在性、惟一性问题,利用不动点方法和线性系统指数二分性理论,得到一些关于该方程的概周期解存在性、惟一性的新结果。The present paper makes a study on existence and uniqueness of almost periodic solutions to a class of nonlinear integro-differential equations with impulses and infinite delays, that is,{x（t）=A（t,x（t））x（t）＋∫-∞C（t,s）g（x,x（s））ds＋m∑i=1f1（t,x（t-τi））＋b（t）,t≠tk,△x（t）=Bkx（t）＋Ik（x（ft））＋yk,t=tk,k∈Z. By using fixed point method and the theory of exponential dichotomy of linear system, the paper obtains some new results on existence and uniqueness of almost periodic solutions to those equations.

关 键 词：无穷时滞:脉冲方程 概周期解 存在性 惟一性 

分 类 号：O175.1[理学—数学]