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浙江大学学报（理学版）
Journal of Zhejiang University (Science Edition)  2024, Vol. 51 Issue (1): 5-13    DOI: 10.3785/j.issn.1008-9497.2024.01.002
Mathematics and Computer Science     
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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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     
Received: 07 March 2022      Published: 10 January 2024
CLC:  O 175.27  
Corresponding Authors: Wenjie SUN     E-mail: chj8121912@sina.com;939512986@qq.com
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Yunhui ZENG
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Yuanhong YU
Cite this article:

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.

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https://www.zjujournals.com/sci/EN/Y2024/V51/I1/5


具阻尼项的二阶非线性中立型微分方程的振动准则

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 
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