Periodic solutions for a fourth-order p-Laplacian neutral functional differential equation

By means of Mawhinʹs continuation theorem, we study a kind of fourth-order p-Laplacian neutral functional differential equation with a deviating argument in the form: ( φ p ( x ( t ) − cx ( t − δ ) ) ″ ) ″ = f ( x ( t ) ) x ′ ( t ) + g ( t , x ( t − τ ( t , | x | ∞ ) ) ) + e ( t ) . Some sufficient criteria to guarantee the existence of periodic solutions are obtained. The significance of this paper is that the growth power imposed on the variable x in function g(t,x) is allowed to be greater than p−1. It is interesting that our results are not only dependent on the deviating argument τ but also dependent on the delay δ .