具拟线性中立项的二阶变时滞动力方程的振动定理

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1492-1503.

具拟线性中立项的二阶变时滞动力方程的振动定理

覃桂茳^1,²(),杨甲山^1,^3,*()

¹ 梧州学院大数据与软件工程学院广西梧州 543002
² 梧州学院广西高校行业软件技术重点实验室广西梧州 543002
³ 梧州学院广西高校图像处理与智能信息系统重点实验室广西梧州 543002

收稿日期:2021-01-18 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 杨甲山 E-mail:57841824@qq.com;syxyyjs@163.com
作者简介:覃桂茳, E-mail: 57841824@qq.com
基金资助:
国家自然科学基金(51765060);广西自然科学基金青年项目(2018JJB170034);广西高校中青年教师基础能力提升项目(2018KY0543);广西高校中青年教师基础能力提升项目(2020KY17007);梧州学院重点科研项目(2016B008);梧州学院重点科研项目(2020B005)

Oscillation Theorems of Second-Order Variable Delay Dynamic Equations with Quasilinear Neutral Term

Guijiang Qin^1,²(),Jiashan Yang^1,^3,*()

¹ School of Data Science and Software Engineering, Wuzhou University, Guangxi Wuzhou 543002
² Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Guangxi Wuzhou 543002
³ Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Guangxi Wuzhou 543002

Received:2021-01-18 Online:2021-10-26 Published:2021-10-08
Contact: Jiashan Yang E-mail:57841824@qq.com;syxyyjs@163.com
Supported by:
the NSFC(51765060);the NSF of Guangxi(2018JJB170034);the Basic Ability Improvement Project of Young and Middle-aged Teachers in Guangxi Universities(2018KY0543);the Basic Ability Improvement Project of Young and Middle-aged Teachers in Guangxi Universities(2020KY17007);the Key Project of Wuzhou University(2016B008);the Key Project of Wuzhou University(2020B005)

摘要/Abstract

摘要：

研究时间测度链上一类具有一个拟线性中立项的二阶动力方程的振动性，利用黎卡提变换技术和一些经典不等式，结合时间测度链上的理论，在正则条件下获得了该类方程振动的若干新定理，这些定理推广、改进且丰富了近年来已有的部分经典研究成果.最后举例说明了定理的应用.

关键词: 振动性, 时间测度链, 拟线性中立项, Riccati变换, 变时滞动力方程

Abstract:

The objective of this paper is to discuss the oscillation of a class of second-order dynamic equations with a quasi-linear neutral term on the time measurement chain. Under the regularity condition, by using the generalized Riccati transformation and the classical inequality, and combining with the time scales theory, some new oscillation theorems for the equations are established. The results obtained extend, improve and enrich the part of the study results established in previous literatures. Finally, examples are given to illustrate the applications of the obtained theorems.

Key words: Oscillation, Time scales, Quasilinear neutral, Riccati transformation, Variable delay dynamic equations

中图分类号:

O175.7

覃桂茳,杨甲山. 具拟线性中立项的二阶变时滞动力方程的振动定理[J]. 数学物理学报, 2021, 41(5): 1492-1503.

Guijiang Qin,Jiashan Yang. Oscillation Theorems of Second-Order Variable Delay Dynamic Equations with Quasilinear Neutral Term[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1492-1503.

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