| 摘要: |
| 基于压缩不动点原理,考虑一类具有脉冲效应的时滞微分方程x'=A(t)x(t+∑i=1n Ai(t)x(t-ri)+h(t),t≠τk,τk〈τk+1,k=±1,±2L,△x(t)=Bkx(t)+Ik(x(t))+pk,t=τk概周期解的存在性问题,在一定条件下获得了系统存在唯一概周期的一组充分条件. |
| 关键词: 微分方程 不动点原理 概周期 存在性 |
| DOI： |
| 投稿时间：2006-09-11 |
| 基金项目:Supported by the National Nature Science Foundation of China(10461003);Scientific Research Foundation of Guangxi EducationOffice (2006243);Young Foundation of Guangxi Yulin NormalUniversity (2007). |
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| Almost Periodic Solutions of Linear Impulsive Delay Differential Equations |
|
LIU Yong-jian1, FENG Chun-hua2
|
| (1.Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi, 537000, China;2.Department of Mathematics, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
| This paper deals with the existence of almost periodic solutions of linear impulsive delay differential equations as follows, x'=A (t)x (t+∑i=1n Ai (t)x (t-ri)+h (t), t≠τk, τk〈τk+1, k=±1, ±2L, △x (t)=Bkx (t)+Ik (x (t))+pk, t=τk, by using the fixed point theorem of contraction mapping prmctple we present a set of sufficient conditions to ensure the existence and uniqueness of almost periodic solutions of impulsive delay differential equations in some closed convex set. |
| Key words: differential equation fixed point theorem almost periodic solution existence and uniqueness |
