无穷时滞非线性中立型高维周期系统的周期解

On Existence of Periodic Solutions to a Class of High Order Nonlinear Neutral Functional Differential Equations with Infinite Delay

通过构造算子讨论了一类具有无穷时滞非线性中立型高维周期微分系统d[(x(t)+c(t)x(t-τ)]/dt=A(t,x(t-τ(t)))x(t)+∫t-∞B(t,s)x(s)ds+sum from i=1 to p gi(t,x(t-τi(t)))+b(t)的周期解问题.通过巧妙地构造算子,利用线性系统的指数二分性和Krasnodelskii不动点定理得到新的周期解存在性的条件.

By means of the Krasnodelskii＇s fixed-point theorem and exponential dichotomy of linear system, the existence of periodic solutions for a class of high order nonlinear neutral functional differential equations with infinite delay d[（x（t）＋c（t）x（t-r）]/dt=A（t,x（t-τ（t）））＋∫-∞^t B（t,s）x（s）ds＋∑i=1^p gi（t,x（t-τi（t）））＋b（t） is investigated; and a set of sufficient conditions to guarantee the existence of periodic solutions of the systems is obtained.