数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 797-811.

• 论文 • 上一篇    下一篇

二阶非线性中立型时滞微分方程的振动性

仉志余1(),俞元洪2,李淑萍3,乔士柱1   

  1. 1 太原工业学院理学系 太原 030008
    2 中国科学院数学与系统科学研究院 北京 100190
    3 中北大学理学院 太原 030051
  • 收稿日期:2017-08-15 出版日期:2019-08-26 发布日期:2019-09-11
  • 作者简介: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);山西省自然科学基金(2011011002-3)

Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay

Zhiyu Zhang1(),Yuanhong Yu2,Shuping Li3,Shizhu Qiao1   

  1. 1 Department of Sciences, Taiyuan Institute of Technology, Taiyuan 030008
    2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
    3 Department of Mathematics, North University of China, Taiyuan 030051
  • Received:2017-08-15 Online:2019-08-26 Published:2019-09-11
  • Supported by:
    the NSFC(11701528);the NSFC(11647034);the Natural Science Foundation of Shanxi Province(2011011002-3)

摘要:

该文研究一类二阶非线性中立型时滞微分方程的振动性,利用双Riccati变换和不等式技巧,得到了所研究方程一切解振动的若干新的充分条件.所得结果推广、改进和统一了最近文献中关于半线性、非线性泛函微分方程和广义Emden-Fowler方程的振动定理.同时也给出了主要定理的相应示例.

关键词: 二阶非线性微分方程, 半线性微分方程, Emden-Fowler方程, 中立型, Riccati变换, 振动准则

Abstract:

In this paper, the oscillatory behavior of solutions to a nonlinear second-order neutral differential equation is to study. Using double Riccati transformation and the technique of inequations, some new sufficient conditions are obtained for the solutions of all oscillations and the results generalize, improve and unify the oscillation theorems of half linear functional differential equations, nonlinear equations and generalized Emden-Fowler type equations in the literature recently. At last, some examples are given to illustrate the effectiveness of our results.

Key words: Second order nonlinear differential equation, Half linear differential equation, Emden-Fowler equation, Neutral, Riccati transformation, Oscillation criterion

中图分类号: 

  • O175