具有无穷时滞的高维中立型泛函微分方程概周期解的存在性  

Existence of Almost Periodic Solutions for a High Order Neutral Functional Differential Equations with Infinite Delay

作　　者：杨健[1] 万舒丽[1] 冯春华[1] 黄健民[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：《石河子大学学报（自然科学版）》2008年第2期257-260,共4页Journal of Shihezi University(Natural Science)

基　　金：国家自然科学基金项目(10461003)

摘　　要：利用线性系统的指数型二分性和Krasnodelskii不动点定理,讨论了一类具有无穷时滞高维中立型泛函微分方程ddt(x(t)+c(t)x(t-τ))=A(t,x(t-τ(t)))x(t)+∫t-∞B(t,s)x(s)ds+i∑=p1gi(t,x(t-τi(t)))+b(t)概周期解的存在性。在较弱的假设条件下得到了该类方程至少存在一个概周期解的定理,推广了已有文献的主要结果。By means of the exponential dichotomy of the linear system and Krasnodelskii＇ s fixed point theorem, this paper discusses the existence of almost periodic solutions for a high order neutral functional differential equations with infinite delay. d/dt（x（t）＋c（t）x（t-τ））=A（t,x（t-τ（t）））x（t）＋∫^t-∞B（t,s）x（s）ds＋p∑i=1gi（t,x（t-τi（t）））＋b（t）.A theorem about the existence of almost periodic solutions to this kind of equation is obtained under the weaker assumptions. The result has been generalized in the literature.

关 键 词：无穷时滞 中立型 泛函微分方程 概周期解 存在性 不动点定理 

分 类 号：O175.1[理学—数学]