Periodic solutions to a second order nonlinear neutral functional differential equation in the critical case

In this paper, the authors study the existence of periodic solutions for a second order neutral functional differential equation(x(t)-cx(t-τ))″=f(x(t))x′(t)+g(t,x(t-μ(t)))+e(t)(x(t)-cx(t-τ))″=f(x(t))x′(t)+g(t,x(t-μ(t)))+e(t)in the critical case |c|=1|c|=1. By employing Mawhin's continuation theorem and some analysis techniques, sufficient conditions are given for the existence of periodic solutions.