二阶哈密顿系统周期解的存在性

IF 1.1 4区数学 Q1 MATHEMATICS

Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.36

Xiao-Feng Ke, Jia‐Feng Liao

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引用次数: 0

摘要

本文研究了二阶哈密顿系统周期解的存在性。通过引入一个新的增长条件，推广了Ambrosetti-Rabinowitz条件，用变分方法证明了非平凡T -周期解的存在性。我们的结果是新的，因为它不仅可以处理超二次情况，而且还可以处理各向异性情况，这种情况允许势能只在一个方向上是超二次增长，而在其他方向上是渐近二次增长。

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On the existence of periodic solutions to second order Hamiltonian systems

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.

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来源期刊

Electronic Journal of Qualitative Theory of Differential Equations 数学-数学

CiteScore

1.40

自引率

9.10%

发文量

审稿时长

3 months

期刊介绍： The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.