ABSTRACT
In this paper, we obtain the existence of infinitely many non-constant periodic solutions with negative fixed energy for a class of second-order Hamiltonian systems, which greatly improves the existing results such as Zhang [Periodic solutions for some second order Hamiltonian systems. Nonlinearity. 2009;22(9):2141–2150, Theorem 1.5]. Moreover, we exhibit two simple and instructive examples to make our result more clear, which have not been solved by known results.
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Acknowledgements
The authors express their sincere gratitude to professor Zhang Shiqing for his helpful suggestions, and also sincerely thank the referees and the editors for their helpful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Jinlong Wei http://orcid.org/0000-0002-9182-4587