Volume 35 • Number 1 • 2012   • Existence of Periodic Solutions of $p(t)$-Laplacian Systems Liang Zhang and Yi Chen Abstract. In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for $p(t)$-Laplacian system \begin{equation*} \left\{ \begin{aligned} &\frac{d}{dt}(|\dot{u}(t)|^{p(t)-2}\dot{u}(t))=\nabla F(t,u(t))\quad \text{a.e. }t\in[0,T] \\ &u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0, \end{aligned} \right. \end{equation*} which generalize some existence theorems. 2010 Mathematics Subject Classification: 34C25, 35A15. Full text: PDF