具有变量时滞的周期微分系统的周期解  

PERIODIC SOLUTIONS OF PERIODIC DIFFERENTIAL SYSTEM WITH VARIABLE DELAY

作　　者：胡永珍[1] 斯力更[2] 

机构地区：[1]北京第二外国语学院,北京100242 [2]内蒙古师范大学,呼和浩特010022

出　　处：《经济数学》2004年第3期272-279,共8页Journal of Quantitative Economics

基　　金：内蒙古自治区自然科学基金资助项目

摘　　要：本文考虑周期微分系统x(t) =A(t,x(t- r1(t) ) ) x(t) + f (t,x (t- r2 (t) ) )的 T-周期解的存在性问题 ,其中 (t,x)∈R× Rn,A(t,x)是 n× n连续矩阵函数 ,f(t,x)是 n维连续向量函数 ,时滞 ri(t) (i=1,2 )是连续函数 ,且 A(t+ T,x) =A(t,x) ,f(t+ T,x) =f(t,x) ,ri(t+ T) =ri(t) (i=1,2 ) ,常数T>0 .本文利用不动点方法 ,建立了保证系统存在 T-周期解的充分条件 ,推广了文 [1- 3]的相关结果 .The existence of periodic solutions of periodic differential periodic system with variable delay(t)=A(t,x(t-r 1(t)))x(t)+f(t,x(t-r 2(t)))are considered,where(t,x)∈R×Rn,the n×n matrix A(t,x) is continuous ,the n-vector f(t,x) is continuous,the delay r i(t)(i=1,2)is continuous,and A(t+T,x)=A(t,x),f(t+T,x)=f(t,x),r i(t+T)=r i(t)(i=1,2),T>0.Using the fixed point method,some sufficient conditions to guarantee the existence of T-periodic solution for the system are established.the related results in [1-3] are extended.

关 键 词：周期微分系统 变量时滞 周期解 

分 类 号：F22[经济管理—国民经济]