一类带阻尼的吸引型奇性Duffing方程周期正解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 131-138.

一类带阻尼的吸引型奇性Duffing方程周期正解的存在性

夏晨阳,王振辉*(),程志波

河南理工大学数学与信息科学学院河南焦作 454003

收稿日期:2021-03-23 出版日期:2022-02-26 发布日期:2022-02-23
通讯作者: 王振辉 E-mail:tiantian@hpu.edu.com
基金资助:
国家自然科学基金(11501170);河南省高校科技创新人才项目(21HASTIT025)

Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type

Chenyang Xia,Zhenhui Wang*(),Zhibo Cheng

School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003

Received:2021-03-23 Online:2022-02-26 Published:2022-02-23
Contact: Zhenhui Wang E-mail:tiantian@hpu.edu.com
Supported by:
the NSFC(11501170);the Scientific and Technological Innovation Talent Project for the Universities of Henan Provience(21HASTIT025)

摘要/Abstract

摘要：

该文考虑了一类带阻尼的吸引型奇性Duffing方程 $ u''(t)+Cu'(t)+g(u(t))=e(t), $ 其中$C$是常数且$C\neq0$，$g$是连续函数并且在原点$x=0$有吸引型奇性.通过应用Manasevich-Mawhin连续定理和一些分析方法, 证明了该方程至少存在一个周期正解.

关键词: Duffing方程, Manasevich-Mawhin定理, 吸引型奇性, 强弱奇性, 周期正解

Abstract:

In this paper, we consider a damped Duffing equation with singularity of attractive type $u''(t)+Cu'(t)+g(u(t))=e(t), $ where $C$ is a constant and $C\neq0$, $g$ is a continuous function and has an attractive singularity at $u=0$. By applications of Manasevich-Mawhin continuation theorem and some analysis skill, we establish some sufficient conditions for the existence of positive $T$-periodic solutions for this equation.

Key words: Duffing equation, Manasevich-Mawhin theorem, Singularity of attractive type, Strong and weak singular, Positive periodic solution

中图分类号:

O175.1

夏晨阳,王振辉,程志波. 一类带阻尼的吸引型奇性Duffing方程周期正解的存在性[J]. 数学物理学报, 2022, 42(1): 131-138.

Chenyang Xia,Zhenhui Wang,Zhibo Cheng. Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type[J]. Acta mathematica scientia,Series A, 2022, 42(1): 131-138.

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