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Periodic solutions for a class of nonautonomous second-order systems. (English) Zbl 1050.34062

The existence of periodic solutions of the nonautonomous second-order system \(\ddot{u}=\nabla F(t,u(t))\), \(t\in [0,T]\), subject to the periodicity conditions \(u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0\), is investigated. Proofs use the least action principle.

MSC:

34C25 Periodic solutions to ordinary differential equations
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