带阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动准则

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 934-946.

带阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动准则

仉志余^1,*(),宋菲菲¹,李同兴²(),俞元洪³

¹ 太原工业学院理学系太原 030008
² 山东大学控制科学与工程学院济南 250061
³ 中国科学院数学与系统科学研究院北京 100190

收稿日期:2019-09-06 出版日期:2020-08-26 发布日期:2020-08-20
通讯作者: 仉志余 E-mail:litongx2007@163.com
作者简介:李同兴, E-mail:litongx2007@163.com
基金资助:
国家自然科学基金(11701528);国家自然科学基金(11747098);国家自然科学基金(61503171);山西省自然科学基金(2011011002-3)

Oscillation Criteria of Second Order Nonlinear Neutral Emden-Fowler Differential Equations with Damping

Zhiyu Zhang^1,*(),Feifei Song¹,Tongxing Li²(),Yuanhong Yu³

¹ Department of Sciences, Taiyuan Institute of Technology, Taiyuan 030008
² School of Control Science and Engineering, Shandong University, Jinan 250061
³ Academy of Mathematics and systems Science, Chinese Academy of Sciences, Beijing 100190

Received:2019-09-06 Online:2020-08-26 Published:2020-08-20
Contact: Zhiyu Zhang E-mail:litongx2007@163.com
Supported by:
the NSFC(11701528);the NSFC(11747098);the NSFC(61503171);the NSF of Shanxi Province(2011011002-3)

摘要/Abstract

摘要：

该文研究一类带有更广泛而不失物理意义阻尼项的二阶非线性中立型Emden-Fowler时滞微分方程的振动性.利用指数函数变换、Riccati变换和不等式技巧，获得了该类方程几个新的振动定理，推广、改进和丰富了已有文献中的研究结果，并逐一给出例子说明了相应定理的实用效果.

关键词: 振动准则, Emden-Fowler方程, 中立型, 非线性微分方程, 阻尼项

Abstract:

In this paper, by using the methods of exponential function transformation, Riccati transformation and inequality techniques, we study the oscillation behavior for a class of second order nonlinear neutral delay Emden-Fowler differential equations with the most extensive and physically meaningful damping term. Several new oscillation theorems which extend and improve some known results in the literature recently are established and some examples are provided to illustrate the relevance of new theorems.

Key words: Oscillation criteria, Emden-Fowler equation, Neutral, Nonlinear differential equation, Damping term

中图分类号:

O175

仉志余,宋菲菲,李同兴,俞元洪. 带阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动准则[J]. 数学物理学报, 2020, 40(4): 934-946.

Zhiyu Zhang,Feifei Song,Tongxing Li,Yuanhong Yu. Oscillation Criteria of Second Order Nonlinear Neutral Emden-Fowler Differential Equations with Damping[J]. Acta mathematica scientia,Series A, 2020, 40(4): 934-946.

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