[1]罗李平.一类带分布时滞的非线性中立型广义弹性杆方程的振动分析[J].南京师大学报(自然科学版),2022,45(04):10-15.[doi:10.3969/j.issn.1001-4616.2022.04.002]
　Luo Liping.Oscillatory Analysis for a Class of Nonlinear Neutral Generalized Elastic-Rod Equations with Distributed Delay[J].Journal of Nanjing Normal University(Natural Science Edition),2022,45(04):10-15.[doi:10.3969/j.issn.1001-4616.2022.04.002]
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一类带分布时滞的非线性中立型广义弹性杆方程的振动分析()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第45卷
期数:
2022年04期
页码:
10-15
栏目:
数学
出版日期:
2022-12-15

文章信息/Info

Title:
Oscillatory Analysis for a Class of Nonlinear Neutral Generalized Elastic-Rod Equations with Distributed Delay
文章编号:
1001-4616(2022)04-0010-06
作者:
罗李平
(衡阳师范学院数学与统计学院,湖南 衡阳 421002)
Author(s):
Luo Liping
(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,China)
关键词:
振动性; 广义弹性杆方程; 分布时滞; 非线性中立型; 偶数阶
Keywords:
oscillation; generalized elastic-rod equation; distributed delay; nonlinear neutral type; even order
分类号:
O175.29; O175.4
DOI:
10.3969/j.issn.1001-4616.2022.04.002
文献标志码:
A
摘要:
基于力学上非线性弹性杆(组)结构的振动问题与数学上偏微分方程(组)振动理论之间的密切联系,研究了一类带分布时滞的偶数阶非线性中立型广义弹性杆方程的振动性问题,建立了该类弹性杆方程在Dirichlet边值条件下所有解振动的新的充分性判据,并给出一个实例阐述结果的有效性. 所得结果反映出该类弹性杆结构在这种情况下的振动状态——它始终发生振动.
Abstract:
Based on the close relationship between the vibration problems of nonlinear elastic rod(systems)structure in mechanics and the oscillation theory of partial differential equation(systems)in mathematics,the oscillation problems for a class of even order nonlinear neutral generalized elastic-rod equations with distributed delays are investigated,and some new sufficient criteria for oscillation of all solutions of such elastic-rod equations are establish under Dirichlet's boundary value condition,which the effectiveness of the results is illustrated by an example. The obtained results reflect the oscillation state of such elastic-rod structure in the case that the oscillation kept happening.

参考文献/References:

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[9]LUO Z G,LUO L P,ZENG Y H. Oscillation results for BVPs of even order nonlinear neutral partial differential equations[J]. Journal of nonlinear modeling and analysis,2019,1(2):261-270.
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　Lin Wenxian.Oscillation of Certain Neutral Hyperbolic Functional Differential Equations With Distributed Deviating Arguments[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(04):13.
[2]林文贤.具分布时滞和阻尼项的三阶中立型微分方程的振动性[J].南京师大学报(自然科学版),2023,46(02):1.[doi:10.3969/j.issn.1001-4616.2023.02.001]
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备注/Memo

备注/Memo:
收稿日期:2022-01-21.
基金项目:湖南省教育厅科研重点项目(21A0440)、湖南省自然科学基金项目(2022JJ90021)、衡阳师范学院学科专项项目(XKZX21002).
通讯作者:罗李平,教授,研究方向:(脉冲)偏微分方程振动理论研究. E-mail:stxyluolp@163.com
更新日期/Last Update: 2022-12-15