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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (4): 469-477.doi: 10.3969/j.issn.1005-3085.2020.04.007

• • 上一篇    下一篇

二阶拟线性中立型时滞微分方程的振动性

李文娟1,2,   李书海1,2,   汤   获1,2   

  1. 1- 赤峰学院数学与统计学院，赤峰  024000
    2- 赤峰学院应用数学研究所，赤峰  024000
  • 收稿日期:2018-04-02 接受日期:2019-02-18 出版日期:2020-08-15 发布日期:2020-10-15
  • 基金资助:
    国家自然科学基金(11761006; 11762001; 11561001)；内蒙古自然科学基金(2017MS0113; 2018MS01026)；内蒙古高校青年科技英才支持计划资助项目(NJYT-18-A14)；内蒙古高等学校科研基金(NJZY17301).

Oscillation of Second Order Quasilinear Neutral Delay Differential Equations

LI Wen-juan1,2,   LI Shu-hai1,2,   TANG Huo1,2   

  1. 1- School of Mathematics and Statistics, Chifeng University, Chifeng 024000
    2- Institute of Applied Mathematics, Chifeng University, Chifeng 024000
  • Received:2018-04-02 Accepted:2019-02-18 Online:2020-08-15 Published:2020-10-15
  • Supported by:
    The National Natural Science Foundation of China (11761006; 11762001; 11561001); the Natural Science Foundation of Inner Mongolia (2017MS0113; 2018MS01026); the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-18-A14); the Higher School Foundation of Inner Mongolia (NJZY17301).

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摘要： 本文主要研究了一类二阶拟线性中立型微分方程的振动性．文中运用广义Riccati变换，积分平均技巧和Hardy-Littlewood-Polya不等式给出了微分方程若干新的振动准则，与其它现有的结果进行比较，所得结果推广和改进了最近一些文献中的关于某些振动性的结果．

关键词: 微分方程, 时滞, 拟线性, 振动性, 二阶

Abstract: In this paper, we mainly study the oscillation of a class of second order quasilinear neutral delay differential equations. By use of the generalized Riccati transformation, integral averaging technique and an inequality due to Hardy-Littlewood-Polya, some new oscillation criteria are established for the equations above. Compare with other existing results, the results extend and improve some known results in the cited literature.

Key words: differential equations, delay, quasilinear, oscillation, second order

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