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Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems

  • * Corresponding author: Jinlong Wei

    * Corresponding author: Jinlong Wei
The first author is partially supported by National Science Foundation of China (116712787) and Graduate Student's Research and Innovation Fund of Sichuan University (2018YJSY045). The third author is partially supported by National Science Foundation of China (11501577, 61773401).
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  • In the past years, there were very few works on the existence of nonconstant periodic solutions with fixed energy of singular second-order Hamiltonian systems, and now we attempt to ingeniously use Ekeland's variational principle to prove the existence of nonconstant periodic solutions with any fixed energy for singular second-order Hamiltonian systems, and our results greatly generalize some well known results such as [1,Theorem 3.6]. Moreover, we exhibit two simple and instructive singular potential examples to make our result more clear, which have not been solved by known results.

    Mathematics Subject Classification: Primary: 70F15, 70H35; Secondary: 34C25, 58E05.

    Citation:

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