一类弱二次Hamilton系统的同宿解的多重性结果

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 364-372.

一类弱二次Hamilton系统的同宿解的多重性结果

孙昭洪¹, 张玮², 贺铁山¹, 高川翔¹

1. 仲恺农业工程学院计算科学学院广州 510225;
2. 玉溪师范学院理学院云南玉溪 653100

收稿日期:2013-10-08 修回日期:2014-05-06 出版日期:2015-04-25 发布日期:2015-04-25
作者简介:孙昭洪,E-mail:sunzh60@163.com;张玮,E-mail:zhw3721@yxnu.net;贺铁山,E-mail:hetieshan68@163.com;高川翔,E-mail:cxg1103@yahoo.com.cn
基金资助:
国家自然科学基金(11401111)和广东省教育科研十二五规划项目(2011TJK468)资助

Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems

Sun Zhaohong¹, Zhang Wei², He Tieshan¹, Gao Chuanxiang¹

1. School of Computational Science, Zhongkai University of Agriculture and Engineering, Guangzhou 510225;
2. Faculty of Sciences, Yuxi Normal University, Yunnan Yuxi 653100

Received:2013-10-08 Revised:2014-05-06 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

考虑二阶非自治弱二次Hamilton系统同宿解的多重性. 一般考虑的势函数关于u在无穷远点处的下界函数是一个正常数. 而当该系数换为一个正函数而非常数时, 情况就会相当不同. 该文中讨论了这一问题, 将此系数推广到下确界可以是0的一个有关t的正函数. 因此该文的结果是对近期一些结果的有意义的改进.

关键词: 下界函数, 弱二次势函数, 多重性, 同宿解

Abstract:

In the present paper we consider the multiplicity of homoclinic solutions for the second order non-autonomous subquadratic Hamiltonian system. In this case, the lower bounded coefficient of the potential function about u near infinity was required to be a positive constant in the literature. However, if the coefficient is a positive function but not a constant, the situation is quite different. In this paper we solved this question. We extent the coefficient to a positive function of t which minimum may be zero. Hence the result in this work is a significant improvement of the results in recent literature.

Key words: Lower bounded coefficient, Subquadratic potential function, Multiplicity, Homoclinic solution

中图分类号:

O211.4

孙昭洪, 张玮, 贺铁山, 高川翔. 一类弱二次Hamilton系统的同宿解的多重性结果[J]. 数学物理学报, 2015, 35(2): 364-372.

Sun Zhaohong, Zhang Wei, He Tieshan, Gao Chuanxiang. Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems[J]. Acta mathematica scientia,Series A, 2015, 35(2): 364-372.

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