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

The purpose of this article is to study the existence of periodic solutions for the p-Laplacian systems with delay \(\begin{aligned} -(|z'(t)|^{p-2}z'(t))'= & {} f(t,z(t+\tau ),z(t),z(t-\tau )),\\ z(\tau )-z(-\tau )= & {} z'(\tau )-z'(-\tau )=0. \end{aligned}\) $$\begin{array}{cc}\hfill -(|z^{\prime }(t){{|}^{p-2}{z}^{\prime }(t))}^{\prime }=& f(t,z(t+\tau ),z(t),z(t-\tau )),\hfill \\ \hfill z(\tau )-z(-\tau )=& z^{\prime }(\tau )-z^{\prime }(-\tau )=0.\hfill \end{array}$$ Using the saddle point theorem and the linking theorem, some new existence theorems are obtained for second-order p-Laplacian systems with delay.