高维无穷时滞脉冲积分微分方程概周期解的存在唯一性  

Existence and Uniqueness of Almost Periodic Solutions to the Higher Dimensional Integro-differential Equation with Impulses and Infinite Delay

作　　者：侯宗毅[1] 林远华[1] 

机构地区：[1]河池学院数学系,广西宜州546300

出　　处：《数学的实践与认识》2009年第12期230-237,共8页Mathematics in Practice and Theory

基　　金：广西教育厅科研基金(200707LX324);河池学院科研课题项目(2008A-N001);河池学院应用数学重点学科(院科研[2007]2号)

摘　　要：研究一类高维无穷时滞的非线性脉冲积分微分方程x′(t)=A(t)x(t)+∫-t∞C(t,s)g(s,x(s))ds+f(t,x(t-τ))+b(t),t≠tkΔx(t)=Bkx(t)+Ik(x(t))+γk,t=tk,k∈Z概周期解的存在性、唯一性问题.利用不动点原理和线性系统的指数二分性理论,建立了保证其概周期解存在性、唯一性的充分条件,得到了一些新的结果.A study is made on existence and uniqueness of almost periodic solutions to a class of nonlinear integro-differential equations with impulses and infinite delay of the following x′（t）=A（t）x（t）＋∫t-∞C（t,s）g（s,x（s））ds＋f（t,x（t-τ））＋b（t）,t≠tkΔx（t）=Bkx（t）＋Ik（x（t））＋γk,t=tk,k∈Z By using fixed point method and the theory of exponential dichotomy of linear system, some sufficient condition that guarantee the existence and uniqueness of almost periodic solution of the system are obtained, Some new results are obtained.

关 键 词：无穷时滞 脉冲方程 概周期解 存在性 唯一性 

分 类 号：O175.8[理学—数学]