华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (1): 1-7.doi: 10.3969/j.issn.1000-5641.201911020

• 数学 • 上一篇    下一篇

一类次线性中立型时滞微分方程的渐近性质

韩忠月1(), 俞元洪2   

  1. 1. 德州学院 数学与大数据学院, 山东 德州　253023
    2. 中国科学院 数学与系统科学研究院, 北京　100190
  • 收稿日期:2019-05-07 出版日期:2021-01-25 发布日期:2021-01-25
  • 作者简介:韩忠月, 女, 教授, 研究方向为微分方程定性理论. E-mail: hanzy699@163.com
  • 基金资助:
    山东省自然科学基金(ZR2017LA012)

Asymptotic properties of a class of delay differential equations with a sub-linear neutral term

Zhongyue HAN1(), Yuanhong YU2   

  1. 1. School of Mathematics and Big Data, Dezhou University, Dezhou Shandong　253023, China
    2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing　100190, China
  • Received:2019-05-07 Online:2021-01-25 Published:2021-01-25

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摘要：

运用广义Riccati变换和中值定理, 讨论了具有阻尼项的次线性中立型时滞微分方程的振动性及渐近性质. 就参数 $\gamma$ 与 $\beta$ 的大小关系和条件 $\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ 的交叉结合在方程振动性的作用方面做了分析, 得到了该方程存在振动解的充分条件, 推广和改进了已有结果, 并用实例给出了其应用.

关键词: 阻尼项, 时滞, 次线性中立型, 微分方程, 振动性

Abstract:

This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition $\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ and the relationship of parameters $\gamma$ and $\beta$ in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly, some applications are given to illustrate the significance of these results.

Key words: damping, delay, sub-linear neutral terms, differential equations, oscillation

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