具有变量时滞的高维周期系统的周期解  

PERIODIC SOLUTIONS OF HIGHER DIMENSIONAL PERIODIC DIFFERENTIAL SYSTEM WITH VARIABLE 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科学学院,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）》2004年第2期107-111,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：内蒙古自然科学基金资助项目 ( 2 0 0 10 90 1-0 6)

摘　　要：考虑高维周期系统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 .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 。The existence of periodic solutions of higher dimensional periodic system with variable delay x[DD(Y-1.5mm]·(t)=A(t,x(t-r_1(t)))x(t)+f(t,x(t-r_2(t))) is considered,where (t,x)∈R×R^n,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.By using the fixed point method,some sufficient conditions to guarantee the existence of T-periodic solutions for the system are (established),and the related results in [1～5] are extended.

关 键 词：变量时滞 高维周期系统 周期解 特征根 全连续算子 Leray—Schauder不动点定理 

分 类 号：O175.14[理学—数学]