一类脉冲延滞微分方程正周期解存在的充分条件

Sufficient Conditions of Positive Periodic Solutions of a Class of Delay Differential Equation with Impulse

运用Brouwer不动点定理,讨论得到了脉冲微分方程x′(t)=-α(t)x(t)+β(t)f(γ(t)x(t-mω)),t>0,t≠tk,x(tk+)-x(tk)=bkx(tk),k=1,2,…,在延滞和非延滞情形下正周期解存在的充分条件.

By applying the Brouwer fixed point theorem, this paper obtains the sufficient conditions for the existence of positive periodic solutions to the impulsive differential equations of the form{x＇（t）=-α（t）x（t）＋β（t）f（γ（t）x（t-mω））.t〉0,t≠tk, x（tk^＋）-x（tk）=bkx（tk）,k=1,2,……,in delay and undelay cases.