数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1041-1054.

• 论文 • 上一篇    

二阶广义Emden-Fowler型延迟微分方程的振荡性分析

李继猛   

  1. 邵阳学院理学院 湖南邵阳 422004
  • 收稿日期:2018-06-18 修回日期:2019-01-06 发布日期:2019-11-08
  • 作者简介:李继猛,E-mail:syxyljm@163
  • 基金资助:
    湖南省自然科学基金(12JJ3008)、湖南省教育厅教学改革研究项目(2016JG671)和邵阳市科技计划项目(2016GX04)

Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations

Li Jimeng   

  1. School of Science, Shaoyang University, Hunan Shaoyang 422004
  • Received:2018-06-18 Revised:2019-01-06 Published:2019-11-08
  • Supported by:
    Supported by the Hunan Natural Science Foundation (12JJ3008), the Research Project on Teaching Reform of Hunan Education Department (2016JG671) and the Science and Technology Plan Project of Shaoyang City (2016GX04)

摘要: 研究了一类二阶广义Emden-Fowler型非线性延迟泛函微分方程的振荡性.利用广义双Riccati变换技术及一些分析技巧,在正则和非正则两种情形下获得了该方程振荡的一系列新准则,推广且改进了现有文献中的一些结果,并给出了3个实例来说明文中的主要结论.

关键词: 振荡性, 延迟, Emden-Fowler型微分方程, Riccati变换

Abstract: We study the oscillatory behavior of a class of second-order generalized EmdenFowler-type nonlinear delay functional differential equations in this paper. By using a couple generalized Riccati transformation and some necessary analytic techniques, we establish some new oscillation criteria for the equations under both the cases canonical form and noncanonical form, which deal with some cases not covered by existing results in the literature. Three examples are given to illustrate the main results of this article.

Key words: Oscillation, Delay, Emden-Fowler-type differential equation, Riccati transformation

中图分类号: 

  • O175.27