On the existence of periodic solutions to Rayleigh differential equation of neutral type 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))+g(t,x(t−μ(t)))+e(t)(x(t)−cx(t−τ))″=f(x′(t))+g(t,x(t−μ(t)))+e(t) in the critical case |c|=1|c|=1. By analyzing some properties of the linear difference operator A:[Ax](t)=x(t)−cx(t−τ)A:[Ax](t)=x(t)−cx(t−τ) and using Mawhin’s continuation theorem, some new results are obtained.