二阶非线性中立型时滞微分方程的振动性

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

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 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 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/Abstract

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

仉志余,俞元洪,李淑萍,乔士柱. 二阶非线性中立型时滞微分方程的振动性[J]. 数学物理学报, 2019, 39(4): 797-811.

Zhiyu Zhang,Yuanhong Yu,Shuping Li,Shizhu Qiao. Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay[J]. Acta mathematica scientia,Series A, 2019, 39(4): 797-811.

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