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Periodic solutions of some non-autonomous second order Hamiltonian systems. (English) Zbl 1157.34324

Summary: We study the existence of periodic solutions of the non-autonomous second order Hamiltonian system
\[ \begin{cases} \ddot u(t)=\nabla F(t,u(t)),\quad &\text{a.e. }t\in [0,T],\\ u(0)-u(T)=\dot u(0)-\dot u(T)=0.\end{cases} \]
We obtain some new existence theorems 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)
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References:

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