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Oscillation criteria for third order neutral Emden–Fowler delay dynamic equations on time scales

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Abstract

This paper is concern with a class of third-order neutral Emden–Fowler dynamic equation

$$\begin{aligned} (a((rz^\Delta )^\Delta )^\alpha )^\Delta (t)+q(t)x^\alpha (\delta (t))=0, \end{aligned}$$

where \(z(t):=x(t)+p(t)x(\tau (t)), \alpha \) is a quotient of odd positive integers. By generalized Riccati transformation and comparison principles, some new criteria which ensure that every solution is oscillatory are established, which improve and supplement some known results in literatures.

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Acknowledgments

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. This research is supported by the Natural Science Foundation of China (61374074, 11571202), Shandong Provincial Natural Science Foundation (ZR2013AL003).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People’s Republic of China

    Yunlong Shi, Zhenlai Han & Chuanxia Hou

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  1. Yunlong Shi
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  2. Zhenlai Han
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Correspondence to Zhenlai Han.

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Shi, Y., Han, Z. & Hou, C. Oscillation criteria for third order neutral Emden–Fowler delay dynamic equations on time scales. J. Appl. Math. Comput. 55, 175–190 (2017). https://doi.org/10.1007/s12190-016-1031-x

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  • DOI: https://doi.org/10.1007/s12190-016-1031-x

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