一类双质子弱耦合碰撞系统的对称周期解

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1427-1439.

一类双质子弱耦合碰撞系统的对称周期解

王梓欢(),王超^*()

盐城师范学院数学与统计学院江苏盐城 224001

收稿日期:2022-01-29 修回日期:2023-02-15 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 王超 E-mail:2539778968@qq.com;wangchaosudamath@163.com
作者简介:王梓欢，Email: 2539778968@qq.com
基金资助:
国家自然科学基金(12071410)

Symmetric and Periodic Solutions for a Class of Weakly Coupled Systems Composed of Two Particles with Obstacles

Wang Zihuan(),Wang Chao^*()

School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu Yancheng 224001

Received:2022-01-29 Revised:2023-02-15 Online:2023-10-26 Published:2023-08-09
Contact: Chao Wang E-mail:2539778968@qq.com;wangchaosudamath@163.com
Supported by:
NSFC(12071410)

摘要/Abstract

摘要：

考虑一类具有两个自由度的弱耦合对称碰撞方程的对称碰撞周期解的存在性、重性问题. 在一类关于时间映射的超线性条件下证明了方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性. 同时, 还给出了一个适合两个自由度的对称碰撞方程的对称碰撞周期解存在的充分条件.

关键词: 对称碰撞方程, 权函数, 对称碰撞周期解, 时间映射, $\rm Poincar\acute{e}$映射

Abstract:

The problems of the existence and multiplicity of symmetric periodic solutions with impact for a class of weakly coupled systems of two degrees of freedom with obstacles are concerned. Under some superlinear assumption on time-mapping, the existence of infinite symmetric harmonic solutions and symmetric subharmonic solutions with impacts of the equation are proved. Furthermore, a sufficient condition for the existence of even and periodic bouncing solution is given for the coupled symmetric impact equations of two degrees of freedom.

Key words: Symmetric equations with obstacles, Weight functions, Symmetric periodic solutions with impacts, Time-mapping, Poincaré mapping

中图分类号:

O175.14

王梓欢,王超. 一类双质子弱耦合碰撞系统的对称周期解[J]. 数学物理学报, 2023, 43(5): 1427-1439.

Wang Zihuan,Wang Chao. Symmetric and Periodic Solutions for a Class of Weakly Coupled Systems Composed of Two Particles with Obstacles[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1427-1439.

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