Some Oscillation Criteria for Higher-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

Ying Sui; Yulong Shi; Yibin Sun; Shurong Sun

doi:10.1051/matecconf/201822801003

All issues

Volume 228 (2018)

MATEC Web Conf., 228 (2018) 01003

Abstract

Open Access

Issue		MATEC Web Conf. Volume 228, 2018 2018 3^rd International Conference on Circuits and Systems (CAS 2018)


Article Number		01003
Number of page(s)		6
Section		Intelligent Computing and Information Processing
DOI		https://doi.org/10.1051/matecconf/201822801003
Published online		14 November 2018

MATEC Web of Conferences 228, 01003 (2018)

Some Oscillation Criteria for Higher-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

Ying Sui, Yulong Shi, Yibin Sun and Shurong Sun^a

College of Sciencel, University of Jinan, Jinan, Shadong 250000, P R China

^a Corresponding author: sshrong@163.com

Abstract

New oscillation criteria are established for higher-order Emdn-Fowler dynamic equation $q (v) x^{β} (δ (v)) + {(r (v) {(z^{Δ^{n - 1}} (v))}^{α})}^{Δ} = 0$ $q(v)x^{\beta } (\delta (v)) + (r(v)(z^{{\Delta ^{{n - 1}} }} (v))^{\alpha } )^{\Delta } = 0$ on time scales, $z (v) : = p (v) x (τ (v)) + x (v)$ $z(v): = p(v)x(\tau (v)) + x(v)$ Our results extend and supplement those reported in literatures in the sense that we study a more generalized neutral delay equation and do not require $r^{Δ} (v) \geq 0$ $r^{\Delta } (v) \ge 0$ and the commutativity of the jump and delay operators.

This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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