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.
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)
关键词
无穷时滞:脉冲方程
概周期解
存在性
惟一性
infinite delay
impulsive equation
almost periodic solutions
existence
uniqueness
