• 论文 •

### 非线性二阶中立型分布时滞微分方程的振动性

1. 1 赤峰学院数学与统计学院 内蒙古赤峰 024000
2 赤峰学院应用数学研究所 内蒙古赤峰 024000
3 中国科学学院数学与系统科学研究院 北京 100190
• 收稿日期:2017-08-27 出版日期:2019-08-26 发布日期:2019-09-11
• 作者简介:李文娟, E-mail:liwenjuan19821015@163.com
• 基金资助:
国家自然科学基金(11761006);国家自然科学基金(11762001);内蒙古自然科学基金(2017MS0113);内蒙古高等学校科研基金(NJZY17300);内蒙古高等学校科研基金(NJZY17301)

### Oscillation of Second Order Nonlinear Neutral Differential Equations with Distributed Delay

Wenjuan Li1,2(),Shuhai Li1,2,Yuanhong Yu3

1. 1 School of Mathematics and Statistics, Chifeng University, Inner Mongolia Chifeng 024000
2 Institute of Applied Mathematics, Chifeng University, Inner Mongolia Chifeng 024000
3 Academy of Mathematics System Sciences, Chinese Academy of Sciences, Beijing 100190
• Received:2017-08-27 Online:2019-08-26 Published:2019-09-11
• Supported by:
the NSFC(11761006);the NSFC(11762001);the Natural Science Foundation of Inner Mongolia(2017MS0113);the Higher School Foundation of Inner Mongolia(NJZY17300);the Higher School Foundation of Inner Mongolia(NJZY17301)

(其中$t\geq t_{0}, ~z(t)=x(t)+\int^{b}_{a}p(t, \xi)x\left(\tau(t, \xi)\right){\rm d}\xi$)的振动性.该文建立了上述方程的若干新的振动准则,所得结果推广和改进了最近一些文献中某些熟知的振动结果,此外,该文给出每个定理所相对应的例子,用来说明其相对于已有文献中的定理具有一定的优越性.

Abstract:

In this work, we study the oscillation of the second order Nonlinear Neutral Differential Equations with Distributed Delay

where $t\geq t_{0}, ~z(t)=x(t)+\int^{b}_{a}p(t, \xi)x(\tau(t, \xi)){\rm d}\xi$. we establish some new oscillation criteria for the above equation. These results extend and improve some known results in the cited literature. Also, our results are illustrated with some examples. It is shown that the theorem has some advantages over the existing literature.

• O175.1