Periodic solutions for a class of second order delay differential systems

Consider the periodic boundary value problem $$\left \{ \textstyle\begin{array}{ll} \ddot{u}(t)+r u(t-\tau)+\nabla F(t, u(t-\tau))=0, \quad\mbox{a.e. } t\in [0,2\tau],\\ u(0)-u(2\tau)=\dot{u}(0)-\dot{u}(2\tau)=0, \end{array}\displaystyle \right . $$ where $\tau>0$ is a given constant, $r\in\mathbf{R}$ is a parameter. Periodic solutions are obtained by using linking theorems.