时间尺度上带超线性中立项的二阶时滞动力方程的振动性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1838-1852.

时间尺度上带超线性中立项的二阶时滞动力方程的振动性

仉志余^1,*(),赵成²,李宇宇¹

¹ 太原工业学院理学系太原 030008
² 内蒙古科技大学信息工程学院内蒙古包头 014010

收稿日期:2020-12-12 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 仉志余 E-mail:zhangzhiyu008@aliyun.com
基金资助:
国家自然科学基金(11701528);国家自然科学基金(11647034);国家自然科学基金(11747098);山西省自然科学基金(2011011002-3)

Oscillation of Second Order Delay Dynamic Equations with Superlinear Neutral Terms on Time Scales

Zhiyu Zhang^1,*(),Cheng Zhao²,Yuyu Li¹

¹ Department of Sciences, Taiyuan Institute of Technology, Taiyuan 030008
² Inner Mongolia University of Science and Technology, Inner Mongolia Baotou 014010

Received:2020-12-12 Online:2021-12-26 Published:2021-12-02
Contact: Zhiyu Zhang E-mail:zhangzhiyu008@aliyun.com
Supported by:
the NSFC(11701528);the NSFC(11647034);the NSFC(11747098);the NSF of Shanxi Province(2011011002-3)

摘要/Abstract

摘要：

该文研究时间尺度上带超线性中立项的二阶时滞动力方程的振动性，运用Riccati变换和Bernoulli不等式等技巧，得到了该方程多个新的振动定理，推广和改进了已有文献中的相应结果，其中几个定理即使对于微分方程也是新的.最后该文分别给出相应的实例验证了所得定理的有效性.

关键词: 振动性, 超线性中立项, 二阶, 时滞动力方程, 时间尺度

Abstract:

In this paper, the oscillation of second order delay dynamic equations with super-linear neutral terms on time scales is studied. By using Riccati transformation and Bernoulli inequality techniques, several new oscillation theorems for the equation are obtained. The corresponding results in the existing literature are generalized and improved, some of which are new even for differential equations. Finally, some examples are given to verify the validity of the theorems.

Key words: Oscillation, Super-linear neutral term, Second order, Delay dynamic equation, Time scale

中图分类号:

O175

仉志余,赵成,李宇宇. 时间尺度上带超线性中立项的二阶时滞动力方程的振动性[J]. 数学物理学报, 2021, 41(6): 1838-1852.

Zhiyu Zhang,Cheng Zhao,Yuyu Li. Oscillation of Second Order Delay Dynamic Equations with Superlinear Neutral Terms on Time Scales[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1838-1852.

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