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浙江大学学报（理学版）
浙江大学学报（理学版）  2024, Vol. 51 Issue (1): 5-13    DOI: 10.3785/j.issn.1008-9497.2024.01.002
数学与计算机科学     
具阻尼项的二阶非线性中立型微分方程的振动准则
曾云辉1,2(),孙文杰2(),罗李平1,俞元洪3
1.衡阳师范学院 数学与统计学院，湖南 衡阳 421002
2.衡阳师范学院南岳学院 数学与计算科学系，湖南 衡阳 421008
3.中国科学院 数学与系统科学研究院, 北京 100190
Oscillation criteria of second order nonlinear neutral differential equations with damping terms
Yunhui ZENG1,2(),Wenjie SUN2(),Liping LUO1,Yuanhong YU3
1.College of Mathematics and Statistics，Hengyang Normal University，Hengyang 421002，Hunan Province，China
2.Department of Mathematics and Computational Sciences，Nanyue College of Hengyang Normal University，Hengyang 421008，Hunan Province，China
3.Academy of Mathematics and System Science，Chinese Academy of Sciences，Beijing 100190，China
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摘要：

建立了二阶非线性中立型阻尼微分方程[a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0的若干振动准则，其中z(t)=x(t)+p(t)x(τ(t))。改进、推广和统一了已有文献的相关结果，并通过实例说明了所得准则的广泛应用效果。
关键词： 振动准则;  阻尼方程;  中立型微分方程;  Emden-Fowler方程;  半线性微分方程    
Abstract:

The purpose of this paper is to establish some new oscillation criteria for the second-order nonlinear neutral differential equations with damping terms which have the form [a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0， where z(t)=x(t)+p(t)x(τ(t)). Our theorems improve, extent and unify a number of related results reported in the literature. The wide application of the obtained criteria is illustrated via examples.
Key words: oscillation criterion    damped equation    neutral differential equation    Emden-Fowler equation    half-linear differential equation
收稿日期: 2022-03-07 出版日期: 2024-01-10
CLC:  O 175.27  
基金资助: 湖南省自然科学基金-衡阳联合基金项目(2022JJ50137);湖南省教育厅科学基金一般项目(23C0234);湖南省双一流应用特色学科项目(湘教通［2018］469);湖南省科技创新计划项目(2016TP1020);湖南省大学生创新创业训练计划项目(S202312659011);衡阳市指导性计划项目(202121014364);衡阳师范学院学科专项(xkzx21002)
通讯作者: 孙文杰     E-mail: chj8121912@sina.com;939512986@qq.com
作者简介: 曾云辉（1978—），ORCID：https：//orcid.org/0000-0003-2620-2738，男，硕士，副教授，主要从事微分方程定性理论研究，E-mail：chj8121912@sina.com.
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引用本文:

曾云辉,孙文杰,罗李平,俞元洪. 具阻尼项的二阶非线性中立型微分方程的振动准则[J]. 浙江大学学报（理学版）, 2024, 51(1): 5-13.

Yunhui ZENG,Wenjie SUN,Liping LUO,Yuanhong YU. Oscillation criteria of second order nonlinear neutral differential equations with damping terms. Journal of Zhejiang University (Science Edition), 2024, 51(1): 5-13.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2024.01.002    或    https://www.zjujournals.com/sci/CN/Y2024/V51/I1/5

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