Periodic solutions for a second order nonlinear functional differential equation

The second order nonlinear delay differential equation with periodic coefficients x″(t)+p(t)x′(t)+q(t)x(t)=r(t)x′(t−τ(t))+f(t,x(t),x(t−τ(t))),t∈R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation.