On the existence of periodic solutions to Rayleigh differential equation of neutral type in the critical case Original Research Article

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) Turn MathJax on 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.