On the existence of periodic solutions to a pp-Laplacian neutral differential equation in the critical case

In this paper, the author studies the existence of periodic solutions for a second order neutral functional differential equation (φp(x(t)−cx(t−τ))′)′=f(x(t))x′(t)+g(t,x(t−μ(t)))+e(t)(φp(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 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.