Periodic solutions for a higher order p-Laplacian neutral functional differential equation with a deviating argument

In this paper, a higher order p-Laplacian neutral functional differential equation with a deviating argument: [φp([x(t)−c(t)x(t−σ)](n))](m)+f(x(t))x′(t)+g(t,x(t−τ(t)))=e(t)[φp([x(t)−c(t)x(t−σ)](n))](m)+f(x(t))x′(t)+g(t,x(t−τ(t)))=e(t) has been studied by applying Mawhin’s continuation degree theorem. Some new criteria to guarantee the existence of periodic solutions are obtained. It is interesting that the power of the variable xx in function gg is allowed to be greater than p−1p−1.