Oscillation for second-order half-linear delay damped dynamic equations on time scales

LI Jimeng; YANG Jiashan

doi:10.13471/j.cnki.acta.snus.2019.04.011

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Oscillation for second-order half-linear delay damped dynamic equations on time scales

更新时间：2023-12-11

- Oscillation for second-order half-linear delay damped dynamic equations on time scales
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 58, Issue 4, Pages: 108-114(2019)
- 作者机构：
  
  1. 邵阳学院理学院,湖南,邵阳,422004
  2. 
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.04.011
  CLC：
- Published：2019，
  
  Published Online：25 July 2019，
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LI Jimeng, YANG Jiashan. Oscillation for second-order half-linear delay damped dynamic equations on time scales. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(4):108-114(2019)
DOI：

LI Jimeng, YANG Jiashan. Oscillation for second-order half-linear delay damped dynamic equations on time scales. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(4):108-114(2019) DOI： 10.13471/j.cnki.acta.snus.2019.04.011.

摘要

研究了时间尺度

上二阶半线性的变时滞阻尼动力方程［a(

)|x

(

λ－1

(

)]

+b(t)|x

(

λ－1

(

)+p(t)|x(δ(t))|

λ－1

x(δ(

))=0 的振动性

考虑方程是非正则情形，即∫

∞

［a

－1

(

－b/a

(s

)］

1/λ

Δs

∞

通过引入广义Riccati变换

借助时间尺度上的微积分理论

并结合不等式技巧

建立了该方程的一些新振动准则

推广、改进并丰富了现有文献中的结果。

Abstract

The oscillation of second-order half-linear variable delay damped dynamic equation［a(

)|x

(

λ－1

(

)]

+b(t)|x

(

λ－1

(

)+p(t)|x(δ(t))|

λ－1

x(δ(

))=0 is investigated on a time scale

in which the equation is noncanonical

i.e.

∫

∞

［a

－1

(

－b/a

(s

)］

1/λ

Δs

∞. By using the generalized Riccati transformation and the calculus theory on the time scales

and in combination with some inequality technique

some new oscillation criteria for the equation are established. It generalizes

improves and enriches the known results.

关键词

振动性时间尺度泛函动力方程Riccati变换变时滞

Keywords

oscillationtime scalesfunctional dynamic equationsRiccati substitutionsvariable delay

references

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Related Author

SUN Shurong



HAN Zhenlai

YANG Jiashan

WANG Qiru

ZHANG Shaoyan

YANG Jiashan

ZHANG Xiaojian

Related Institution

School of Sciences, University of Jinan

Department of Science and Information, Shaoyang University

．广东金融学院

．中山大学数学与计算科学学院

College of Mathematics and Statistics, Hengyang Normal University

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