Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

doi:10.1007/s42967-020-00092-4

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 497-508.doi: 10.1007/s42967-020-00092-4

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Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

Shan Shi, Zhenlai Han

School of Mathematical Sciences, University of Jinan, Jinan 250022, China

收稿日期:2019-09-18 修回日期:2020-07-25 出版日期:2021-09-20 发布日期:2021-09-16
通讯作者: Shan Shi, Zhenlai Han E-mail:hanzhenlai@163.com;shis0410@163.com
基金资助:
This research is supported by the Shandong Provincial Natural Science Foundation of China (ZR2017MA043).

Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

Shan Shi, Zhenlai Han

School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received:2019-09-18 Revised:2020-07-25 Online:2021-09-20 Published:2021-09-16
Contact: Shan Shi, Zhenlai Han E-mail:hanzhenlai@163.com;shis0410@163.com
Supported by:
This research is supported by the Shandong Provincial Natural Science Foundation of China (ZR2017MA043).

摘要/Abstract

摘要： The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form
(r(t)((y(t) + p(t)y(τ(t)))')^α)' + q(t)y^α(σ(t))=0, t ≥ t₀,
when ∫^∞ ${r^{-\frac{1}{\alpha }}}$(s)ds < ∞. We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation. An example is provided to illustrate the results.

关键词: Oscillation theory, Second-order differential equations, Neutral, Advanced argument, Asymptotic behavior

Abstract: The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form
(r(t)((y(t) + p(t)y(τ(t)))')^α)' + q(t)y^α(σ(t))=0, t ≥ t₀,
when ∫^∞ ${r^{-\frac{1}{\alpha }}}$(s)ds < ∞. We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation. An example is provided to illustrate the results.

Key words: Oscillation theory, Second-order differential equations, Neutral, Advanced argument, Asymptotic behavior

中图分类号:

Shan Shi, Zhenlai Han. Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 497-508.

参考文献

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Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

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