## On periodic solutions of non-autonomous second order Hamiltonian systems.(English)Zbl 1224.34126

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

### MSC:

 34C25 Periodic solutions to ordinary differential equations 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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