Existence of Periodic Solutions for a Class of p-Laplacian Systems with Delay

Abstract

The purpose of this article is to study the existence of periodic solutions for the p-Laplacian systems with delay

$$\begin{aligned} -(|z'(t)|^{p-2}z'(t))'= & {} f(t,z(t+\tau ),z(t),z(t-\tau )),\\ z(\tau )-z(-\tau )= & {} z'(\tau )-z'(-\tau )=0. \end{aligned}$$

Using the saddle point theorem and the linking theorem, some new existence theorems are obtained for second-order p-Laplacian systems with delay.