Periodic solutions for second order Hamiltonian systems (Q713490)

The authors consider the periodic boundary value problem for the Hamiltonian system \[ \begin{aligned} &\ddot {u}(t)=\nabla F(t,u(t))\; \; \text{for a.e. } t\in [0,T], \\ &u(0)-u(T)=\dot {u}(0)-\dot {u}(T=0)\end{aligned} \] and establish some existence theorems for periodic solutions. They use the technique of the least-action principle and the minimax method in critical point theory. The results extend those of \textit{Z. Wang} and \textit{J. Zhang} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 12, 4480--4487 (2010; Zbl 1206.34060)].