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On periodic solutions of non-autonomous second order hamiltonian systems

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Abstract

The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system

$$ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right. $$

Some new existence theorems are obtained by the least action principle.

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Authors and Affiliations

  1. School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan, 410083, P.R.China

    Xingyong Zhang & Yinggao Zhou

  2. School of Information Science and Engineering, Central South University, Changsha, Hunan, 410083, P.R.China

    Yinggao Zhou

Authors
  1. Xingyong Zhang
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  2. Yinggao Zhou
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Correspondence to Xingyong Zhang.

Additional information

This work was supported by the Graduate degree thesis Innovation Foundation of Central South University (No. 3960-71131100014), the Outstanding Doctor degree thesis Implantation Foundation of Central South University (No. 2008yb032), and by the Postdoctoral Science Foundation of Central South University.

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Zhang, X., Zhou, Y. On periodic solutions of non-autonomous second order hamiltonian systems. Appl Math 55, 373–384 (2010). https://doi.org/10.1007/s10492-010-0013-9

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  • DOI: https://doi.org/10.1007/s10492-010-0013-9

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