含n个滞量的微分差分方程周期解的存在性

The Existence of Periodic Solutions of Differential Difference Equations with n Time Lags

通过构造多元函数,定性分析一个耦合自治常微分方程组周期解的存在性,研究含多个滞量的微分差分方程x′(t)=F(x(t),x(t-τ1),x(t-τ2),...,x(t-τn))和x′(t)=F(x(t),x(t-τ),x(t-2τ),...,x(t-nτ))周期解的存在性问题,获得系统存在非平凡振动周期解的一组充分条件,推广和改进了文献[3～5]的结果.

By constructing multivariate function and qualitative analyzing the existence of periodic solutions of a coupled system of autonomous system of differential equations, the existence of nonconstant oscillating periodic solutions of differential difference equations with n time lags x′（t）=F（x（t）,x（t-τ1）,x（t-τ2）,...,x（t-τn）） and x′（t）=F（x（t）,x（t-τ）,x（t-2τ）,…,x（t-nτ）） is studied. A set of sufficient conditions on the existence is obtained, the results of Reference [3~5] are extended and improved.