On the existence of periodic solutions to second order Hamiltonian systems

Ke Xiao-Feng and Liao Jia-Feng: On the existence of periodic solutions to second order Hamiltonian systems. (2022)

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In this paper, the existence of periodic solutions to the second order Hamiltonian systems is investigated. By introducing a new growth condition which generalizes the Ambrosetti–Rabinowitz condition, we prove a existence result of nontrivial T-periodic solution via the variational methods. Our result is new because it can deal with not only the superquadratic case, but also the anisotropic case which allows the potential to be superquadratic growth in only one direction and asymptotically quadratic growth in other directions.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 36
ISSN: 1417-3875
Number of Pages: 12
Language: English
Place of Publication: Szeged
Uncontrolled Keywords: Hamilton rendszerek - másodrendű, Differenciálegyenlet
Additional Information: Bibliogr.: p. 9-12. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. Sep. 08. 15:35
Last Modified: 2022. Nov. 08. 08:31
URI: http://acta.bibl.u-szeged.hu/id/eprint/76537

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