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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 ›› 2016, Vol. 33 ›› Issue (2): 206-220.doi: 10.3969/j.issn.1005-3085.2016.02.010

• • 上一篇    

时间尺度上三阶非线性中立型动力方程的振动准则(英)

仉志余1,   韩   强2,   俞元洪3   

  1. 1- 太原工业学院理学系，太原  030008
    2- 山东大学数学学院，济南  250100
    3- 中国科学院数学与系统科学研究院，北京 100190
  • 收稿日期:2014-05-23 接受日期:2015-11-06 出版日期:2016-04-15 发布日期:2015-06-15
  • 基金资助:
    山西省自然科学基金 (2011011002-3).

Oscillation Criteria for Third-order Nonlinear Neutral Dynamic Equations on Time Scales

ZHANG Zhi-yu1,  HAN Qiang2,  YU Yuan-hong3   

  1. 1- Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    2- School of Mathematics, Shandong University, Jinan 250100
    3- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
  • Received:2014-05-23 Accepted:2015-11-06 Online:2016-04-15 Published:2015-06-15
  • Supported by:
    The Natural Science Foundation of Shanxi Province (2011011002-3).

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摘要： 源于电子工程、机械工程、生态工程和航天工程等领域的许多问题均可用时间尺度上的动力方程来描述，因此，研究这类方程有着重要的理论价值和实际意义．本文利用广义Riccati变换，积分平均和比较原理，研究了一类时间尺度上三阶非线性中立型时滞动力方程的振动性和渐近性，给出了这类方程新的Kamenev型振动准则和Philos型振动准则．本文成果推广了已知文献的多个相应结果并给出了例证．

关键词: 三阶非线性动力方程, 中立型, 振动准则, 渐近性, 广义Riccati变换, 时间尺度

Abstract:

Many practical problems, such as those from electronic engineering, mechanical engineering, ecological engineering, aerospace engineering and so on, need to be described by dynamic equations on time scales, so it is important in theory and practical significance to study these equations. In this paper, the oscillation and asymptotic behavior of third-order nonlinear neutral delay dynamic equations on time scales are studied by using generalized Riccati transformation technique, integral averaging methods and comparison theorems. The main purpose of this paper is to establish some new oscillation criteria for such dynamic equations. The new Kamenev criteria and Philos criteria are given, and an example is considered to illustrate our main results.

Key words: third-order nonlinear dynamic equation, neutral, oscillation criterion, asymptotic behavior, generalized Riccati transformation, time scale

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