一类高维时滞微分方程的周期解

Periodic Solutions for a Class of Higher Dimensional Delay Differential Equations

中文关键词:  时滞微分方程  周期时滞  周期解

英文关键词:delay differential equation  periodic deley  periodic solution.

中文摘要:

      本文考虑高维时滞微分方程ｘ′（ｔ）＝Ａ（ｔ，ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ，ｘ（ｔ－ｒ（ｔ）））其中（ｔ，ｘ）∈Ｒ^ｎ，Ａ（ｔ，ｘ）是ｎ×ｎ连续矩阵，ｆ（ｔ，ｘ）是ｎ维连续向量，ｒ（ｔ）是时间依赖的滞量，应用不动点定理，在确定的条件下，证明了该系统的周期解的存在性与唯一性

英文摘要:

      In this paper, higher dimensional delay differential equations of the form x′(t)=A(t,x(t))x(t)+f(t,x(t-r(t))) are considered, where the n×n matrix A(t,x) and the n vector f(t,x) are continuous in (t,x)∈R×R^ｎ,r(t) is a delay depending on time t . Using fixed point method, existence and uniqueness of periodic solutions to the above system are proved under defined conditions.