无 Palais-Smale 条件的超二次自洽哈密顿系统的最小周期解

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-09-12 DOI:10.1016/j.jde.2024.09.005

Yuming Xiao , Gaosheng Zhu

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引用次数: 0

摘要

在本文中，我们证明了在弱内哈里条件而非安布罗塞蒂-拉宾诺维茨条件下，偶数二阶哈密顿系统和凸一阶哈密顿系统存在任意规定最小周期 T>0 的周期解。为此，我们将发展奈哈里流形方法，直接处理经常出现的奈哈里集不是流形的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition

In this paper, we prove the existence of periodic solutions with any prescribed minimal period $T > 0$ for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari set is not a manifold.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics