Abstract
The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system $$ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \end{gathered} \right. $$ Some new existence theorems are obtained by the least action principle.
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