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Keywords:
periodic solution; critical point; non-autonomous second-order system; Sobolev inequality
Summary:
The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system \begin {equation*} \begin {cases} \ddot u(t)=\nabla F(t,u(t)),\enspace \text {a.e.} \ t\in [0,T],\\ u(0)-u(T)=\dot u(0)-\dot u(T)=0. \end {cases} \end {equation*} Some new existence theorems are obtained by the least action principle.
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