一类n维变系数方程组的周期解

Periodic Solutions to One Kind of n Dimension Variant Coeffecient Equations

通过对系统x′(t)=A(t)x(t)+g(t)的2π-周期解的讨论,给出其周期解界的估计式,再结合Shauder不动点原理研究了下列系统x′(t)=A(t)x(t)+f(t,x(t-τ(t)))周期解的存在性以及周期解界的估计.

In this paper, through discussing the following Variable Coeffcient equations x′（t）=A（t）x（t）＋g（t） we give an estimation for Me bound of its 2π-periodic solution. Then we use Shauder＇ s fixed point theorem to study the periodic solution to the following nonlinear equations x′（t）=A（t）x（t）＋f（t,x（t-τ（t）））some new results on the existence of periodic solutions are obtained.