具有次线性中立项的二阶阻尼微分方程的振动准则

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 58-69.

具有次线性中立项的二阶阻尼微分方程的振动准则

李文娟^1,²(),汤获²,俞元洪³

¹ 赤峰学院数学与计算机科学学院内蒙古赤峰 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:2021-04-25 出版日期:2022-02-01 发布日期:2022-02-23
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);内蒙古自然科学基金(2021MS01002);内蒙古高等学校科研基金(NJZY17301);赤峰学院科研创新团队-“复分析与非线性动力系统科研创新团队”(cfxykycxtd202005)

Oscillation Criterion for Second Order Damped Differential Equation with a Sublinear Neutral Term

Wenjuan Li^1,²(),Huo Tang²,Yuanhong Yu³

¹ Mathematics and Computer Science College, 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:2021-04-25 Online:2022-02-01 Published:2022-02-23
Supported by:
the NSFC(11761006);the NSFC(11762001);the NSF of Inner Mongolia(2017MS0113);the NSF of Inner Mongolia(2021MS01002);the Higher School Foundation of Inner Mongolia(NJZY17301);the Research and Innovation Team of Complex Analysis and Nonlinear Dynamic Systems of Chifeng University(cfxykycxtd202005)

摘要/Abstract

摘要：

该文研究如下具有次线性中立项的二阶阻尼微分方程的振动性 $ (a (t)(z'(t))^{\gamma})'+b (t)(z'(t))^{\gamma}+q (t) x^{\beta}(\sigma (t))=0, $ 其中$ z (t)=x (t)+p (t) x^{\alpha}(\tau (t))$.利用广义Riccati变换和不等式技巧建立了所考虑方程的新的振动准则.所得结果改进，推广了某些熟知的结果.也给出阐述所得结果意义的若干例子.

关键词: 次线性中立项, Emden-Fowler方程, 半线性微分方程, 中立型微分方程, 振动性

Abstract:

In this work, we consider the oscillation of the second order damped differential equation with a sublinear neutral term $(a(t)(z'(t))^{\gamma})'+b(t)(z'(t))^{\gamma}+q(t)x^{\beta}(\sigma(t))=0, $ where $z(t)=x(t)+p(t)x^{\alpha}(\tau(t)) $. By using the generalized Riccati transformation and integral averaging technique, we establish some new oscillation criteria. These results extend and improve some known results. Examples are also provided to illustrate the application of the conclusions.

Key words: Sublinear neutral term, Emden-Fowler equation, Half-linear differential equation, Neutral differential equation, Oscillation

中图分类号:

O175.1

李文娟,汤获,俞元洪. 具有次线性中立项的二阶阻尼微分方程的振动准则[J]. 数学物理学报, 2022, 42(1): 58-69.

Wenjuan Li,Huo Tang,Yuanhong Yu. Oscillation Criterion for Second Order Damped Differential Equation with a Sublinear Neutral Term[J]. Acta mathematica scientia,Series A, 2022, 42(1): 58-69.

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