具有时滞的周期微分系统的周期解  

PERIODIC SOLUTIONS OF PERIODIC DIFFERENTIAL SYSTEM WITH DELAY

作　　者：胡永珍[1] 斯力更[1] 

机构地区：[1]内蒙古师范大学数学系,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2003年第4期311-315,323,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：内蒙古自治区高校科学研究基金资助项目(2D0002)

摘　　要：考虑周期微分系统x·(t)=A(t,x(t-r1))x(t)+f(t,x(t-r2))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,A(t+T,x)=A(t,x),f(t+T,x)=f(t,x),且T>0,r1,r2∈R.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,改进和推广了文[1～4]的相关结果.The existence of periodic solutions of periodic differential system with delay x·(t)=A(t,x(t-r_1))x(t)+f(t,x(t-r_2)) are considered,where (t,x)∈R×R^n,the n×n matrix A(t,x) is continuous,the n-vector f(t,x) is continuous,A(t+T,x)=A(t,x),f(t+T,x)=f(t,x),and T>0,r_1,r_2∈R.Some sufficient conditions to guarantee the existence of T-periodic solution for the system are established,the related results in are improved and extended.

关 键 词：周期微分系统 时滞 周期解 连续矩阵函数 

分 类 号：O175.14[理学—数学]