Existence of positive periodic solutions for an impulsive differential equation

In this paper, we consider the impulsive differential equation {x′(t)=−a(t)x(t)+p(t)f(t,x(t−τ0(t)),x(t−τ1(t)),…,x(t−τn(t)))a.e,t>0,t≠tk;x(tk+)−x(tk)=bkx(tk)k=1,2,…. By using a fixed point theorem, some criteria are established for the existence of a positive ωω-periodic solution of the above equation. Our work extends and improves some known results.