Liang Zhang,
X. H. Tang
(2013)

In this paper, we deal with the existence of periodic solutions of the $p\left(t\right)$-Laplacian Hamiltonian system $$\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\left(\right|\dot{u}\left(t\right){|}^{p\left(t\right)-2}\dot{u}\left(t\right))=\nabla F(t,u\left(t\right))\phantom{\rule{1.0em}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in [0,T],\hfill \\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0.\hfill \end{array}\right.$$
Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.