Geodesic
On periodic solutions of non-autonomous second order Hamiltonian systems
Applications of Mathematics, Tome 55 (2010) no. 5, pp. 373-384.

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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.
DOI : 10.1007/s10492-010-0013-9
Classification : 34C25, 37J45, 47J30, 58E50
Keywords: periodic solution; critical point; non-autonomous second-order system; Sobolev inequality 
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Zhang, Xingyong; Zhou, Yinggao. On periodic solutions of non-autonomous second order Hamiltonian systems. Applications of Mathematics, Tome 55 (2010) no. 5, pp. 373-384. doi : 10.1007/s10492-010-0013-9. http://geodesic.mathdoc.fr/articles/10.1007/s10492-010-0013-9/

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