非线性二阶中立型分布时滞微分方程的振动性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 812-822.

非线性二阶中立型分布时滞微分方程的振动性

李文娟^1,²(),李书海^1,²,俞元洪³

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 Li^1,²(),Shuhai Li^1,²,Yuanhong Yu³

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)

摘要/Abstract

摘要：

该文主要研究了非线性二阶中立型分布时滞微分方程

$\left(r(t)|z'(t)|^{\alpha-1}z'(t)\right)'+\int^{d}_{c}f\left(t, x\left(\sigma(t, \xi)\right)\right){\rm d}\xi=0$

(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.

关键词: 分布时滞, 半线性, 振动准则, 广义Riccati不等式

Abstract:

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

$(r(t)|z'(t)|^{\alpha-1}z'(t))'+\int^{d}_{c}f(t, x(\sigma(t, \xi))){\rm d}\xi=0, $

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.

Key words: Distributed delay, Half-linear, Oscillation criterion, Generalized Riccati inequality

中图分类号:

O175.1

李文娟,李书海,俞元洪. 非线性二阶中立型分布时滞微分方程的振动性[J]. 数学物理学报, 2019, 39(4): 812-822.

Wenjuan Li,Shuhai Li,Yuanhong Yu. Oscillation of Second Order Nonlinear Neutral Differential Equations with Distributed Delay[J]. Acta mathematica scientia,Series A, 2019, 39(4): 812-822.

参考文献 13

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