中立型标量积分微分方程的周期解(英文)  

Periodic Solutions of Scalar Neutral Integro-Differential Equation

作　　者：陈凤德[1] 孙德献[1] 陈晓星[1] 

机构地区：[1]福州大学数学系,福建福州350002

出　　处：《数学研究》2003年第4期345-350,共6页Journal of Mathematical Study

基　　金：The author is supported by the Fundation of Ability Person of Fuzhou Univcrsity by thegrants(0030824228);the Fundation of Developing Science and Technology of Fuzhou University underthe grants 2003-XQ-21 ; the Foundation of Fujian Education Bureau

摘　　要：本文考虑中立型标量方程的周期的存在唯一性问题.其中a是连续函数,f是R×R 上的连续函数,g(l,s,x)和h(l,s,x)是R×R×R上的连续函数,以及a(l+T)=a(t),g(l+T,s+T,x)=g(l,s,x),h(l+T,s+T,x)=h(l,s,x),f(l+T,x)=f(l,x).通过利用线性系统解的估计式和泛函分析的方法,我们得到保证上述系统周期解存在和唯一的充分性条件.This paper deals with the existence and uniqueness of periodic solutions of scalar neutral integro-differential equation with infinite delay of the form where a is continuous function , f is continuous function on R ×R , g (l ,s,x ) and h(l,s,z) are continuous functions on R×R×R, also a(t+T)=a(t), g (t+T , s+T ,x)=g (l,s,x) ,h(t+T , s+T , x) = h(t,s,x), f(l+T, x )=f(l,x). The sufficient conditions for the existing unique periodic solution of the equation are obtained by using functional analysis method and the estimated formulas of solutions of the linear scalar system.

关 键 词：周期解 存在性 唯一性 无穷时滞 中立型积分微分方程 

分 类 号：O175[理学—数学]