Research on Periodic Solutions of Non-autonomous Second-order Hamiltonian Systems

Journal: Journal of Higher Education Research DOI: 10.32629/jher.v5i2.2402

Yuyue Chen

School of Mathematics, Southeast University, Nanjing, Jiangsu, China

Abstract

In the field of nonlinear science, Hamiltonian systems are crucial models extensively applied in engineering, physics, and biology. The existence of periodic solutions in non-autonomous second-order Hamiltonian systems, as a relatively specialized form, has been a focal and challenging research area. This paper employs variational methods to analyze the existence of periodic solutions in such systems, aiming to provide insights for related research endeavors.

Keywords

second-order non-autonomous hamiltonian systems; periodic solutions; variational methods; principle of least action; local surround theorem; saddle point theorem; mountain pass lemma

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References

[1] Li Yongchang, Liu Chungeng. Existence of periodic solutions for second-order discrete Hamiltonian systems. Journal of Nankai University (Natural Science Edition), 2023, 56(04): 61-70.
[2] Jiang Shan. Existence and multiplicity of periodic solutions for several classes of damped vibration systems. Dissertation, Liaocheng University, 2023.
[3] Li Yongchang. Existence of periodic solutions for second-order discrete Hamiltonian systems. Dissertation, Guangzhou University, 2023.
[4] Chen Xueting. Ground state solutions and minimal periodic solutions of second-order Hamiltonian systems. Dissertation, Guangzhou University, 2023.
[5] Zhong Yuyou. Existence and multiplicity of periodic solutions for second-order non-autonomous Hamiltonian systems. Dissertation, Guangzhou University, 2021.
[6] Gao Cuifeng. Existence of solutions for non-autonomous second-order Hamiltonian systems. Dissertation, Qufu Normal University, 2020.
[7] Chen Yusong, Chang Hejie. Existence and multiplicity of periodic solutions for a class of non-autonomous second-order Hamiltonian systems. Mathematical Quarterly (English Edition), 2019, 34(04): 382-396.
[8] Gao Cuifeng, Mao Anmin. Existence and multiplicity of periodic solutions for a class of non-autonomous second-order Hamiltonian systems. Journal of Binzhou University, 2019, 35(04): 36-44.

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