On periodic solutions of non-autonomous second order hamiltonian systems

The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right. $$\end{document} Some new existence theorems are obtained by the least action principle.