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Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale

  • Qiaoshun Yang EMAIL logo , Zhiting Xu and Ping Long
Published/Copyright: April 28, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In this paper, we consider the oscillation for the second-order quasi-linear neutral dynamic equation

(r(t)|ZΔ(t)|α−1ZΔ(t))Δ+q(t)|x(δ(t))|β−1x(δ(t))=0.

on time scale 𝕋, where Z(t) = x(t) + p(t)x(τ(t)), α,β > 0 are constants. We establish some new oscillation criteria and give sufficient conditions to insure that all solutions of quasi-linear neutral dynamic equation are oscillatory on time scale 𝕋. The new oscillation criteria are presented that improve some known results in the literature.

Key words: oscillation; neutral dynamic equation; time scale
MSC: Primary 34K11; 34C10; 39A11; 34C15

This project was supported by Foundation of Hunan Educational Committee (Grant No. 13C753).

Acknowledgement

We are grateful to the anonymous referees for their careful reading and helpful comments which led to an improvement of our original manuscript.

  1. This paper has been communicated by Michal Fečkan

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Received: 2013-7-24
Accepted: 2013-10-5
Published Online: 2016-4-28
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0128
Keywords for this article
oscillation; neutral dynamic equation; time scale

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  5. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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