一阶带线性部分Hamilton系统的周期解

数学物理学报 ›› 2013, Vol. 33 ›› Issue (5): 894-905.

一阶带线性部分Hamilton系统的周期解

张兴永

昆明理工大学理学院数学系昆明 650500

收稿日期:2011-10-21 修回日期:2013-02-13 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
昆明理工大学人才培养项目(KKSY201207032)资助.

Periodic Solutions for the First Order Hamiltonian System with Linear Part

ZHANG Xing-Yong

Department of |Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming 650500

Received:2011-10-21 Revised:2013-02-13 Online:2013-10-25 Published:2013-10-25
Supported by:
昆明理工大学人才培养项目(KKSY201207032)资助.

摘要/Abstract

摘要：

利用极小极大原理来研究一阶带线性部分Hamilton系统周期解的存在性与多重性问题. 当线性部分正定时, 在较弱的条件下, 利用广义山路引理, 得到系统至少有一个非常数周期解. 此外, 当位势函数是偶函数时, 利用喷泉定理, 得到系统有无穷多个非常数周期解.

关键词: Hamilton系统, 周期解, 广义山路引理, 喷泉定理

Abstract:

In this paper, we consider the existence and multiplicity of periodic solutions for the first order Hamiltonian system with linear part by using the minimax methods. When the linear part is definite, under weaker condition than known ones, by using the generalized Mountain Pass Lemma, we obtain the system has at least one nonconstant periodic solution. Moreover, when the potential is even, by using the Fountain Theorem, we obtain that system has infinitely many nonconstant periodic solutions.

Key words: Hamiltonian system, Periodic solution, Critical point, Generalized Mountain Pass Lemma, Fountain Theorem

中图分类号:

37J45

张兴永. 一阶带线性部分Hamilton系统的周期解[J]. 数学物理学报, 2013, 33(5): 894-905.

ZHANG Xing-Yong. Periodic Solutions for the First Order Hamiltonian System with Linear Part[J]. Acta mathematica scientia,Series A, 2013, 33(5): 894-905.

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