On the existence of periodic solutions to second order Hamiltonian systems

被引：1

作者：

Ke, Xiao-Feng ^{[1
]}

Liao, Jia-Feng ^{[2
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] China West Normal Univ, Coll Math Educ, Nanchong 637002, Sichuan, Peoples R China

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2022年 / 36期

基金：

中国国家自然科学基金;

关键词：

second order Hamiltonian systems; periodic solutions; existence; variational method;

D O I：

10.14232/ejqtde.2022.1.36

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the existence of periodic solutions to the second order Hamil-tonian systems is investigated. By introducing a new growth condition which gener-alizes 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 po-tential to be superquadratic growth in only one direction and asymptotically quadratic growth in other directions.

引用

页码：1 / 12

页数：12

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