[1]王 峰.含小参数微分方程的动力学性质[J].常州大学学报(自然科学版),2020,32(04):71-76.[doi:10.3969/j.issn.2095-0411.2020.04.010]
　WANG Feng.Dynamic Properties of Differential Equations with a Small Parameter[J].Journal of Changzhou University(Natural Science Edition),2020,32(04):71-76.[doi:10.3969/j.issn.2095-0411.2020.04.010]
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含小参数微分方程的动力学性质()
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常州大学学报(自然科学版)[ISSN:2095-0411/CN:32-1822/N]

卷:
第32卷
期数:
2020年04期
页码:
71-76
栏目:
数理科学
出版日期:
2020-07-28

文章信息/Info

Title:
Dynamic Properties of Differential Equations with a Small Parameter
文章编号:
2095-0411(2020)04-0071-06
作者:
王 峰
(常州大学 阿里云大数据学院,江苏 常州 213164)
Author(s):
WANG Feng
(Aliyun School of Big Data, Changzhou University, Changzhou 213164, China)
关键词:
小参数;  微分方程;  动力学性质;  稳定性
Keywords:
small parameter;  differential equation;  dynamic properties;  stability
分类号:
O 175.13
DOI:
10.3969/j.issn.2095-0411.2020.04.010
文献标志码:
A
摘要:
针对含小参数微分方程x¨+εp(t)x=q(t)xβ,采用平均方法和三阶近似方法,获得其动力学性质,包括周期解的存在性、不存在性、稳定性和不稳定性。这里β>0,β≠1,ε>0为小参数,p,q为连续的T-周期函数。与已有文献相比较,本文获得的周期解是非平凡解,并得到稳定性结果。
Abstract:
We are concerned with the dynamic properties for the class of differential equation x¨+εp(t)x=q(t)xβ. Dynamic properties include existence, nonexistence, stability and instability. Here β>0,β≠1,ε>0 is a small parameter and p,qare continuous T-periodic functions. Our results are proved using the averaging method and the third approximation method. Compared with the existing literature, the periodic solutions obtained in this paper are nontrivial and the stability results are obtained.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-12-08。
基金项目:国家自然科学基金资助项目(11861028); 国家自然科学基金青年基金资助项目(11501055)。
作者简介:王峰(1979—),男,江苏泰州人,博士,副教授。E-mail:fengwang@cczu.edu.cn
引用本文:王峰. 含小参数微分方程的动力学性质[J]. 常州大学学报(自然科学版),2020,32(4):71-76.
更新日期/Last Update: 2020-07-30