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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3

# Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

Xin Wu
• College of Information and Statistics Guangxi University of Finance and Economics Nanning, Guangxi 530003 P.R. CHINA
• Other articles by this author:
/ Taixiang Sun
• Corresponding author
• College of Information and Statistics Guangxi University of Finance and Economics Nanning, Guangxi 530003 P.R. CHINA
• Email
• Other articles by this author:
Published Online: 2016-08-26 | DOI: https://doi.org/10.1515/ms-2015-0166

## Abstract

In this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equation $Rn△(t,x(t))+b(t)|Rn−1△(t,x(t))|γ−1Rn−1△(t,x(t))+q(t)f(|x(τ(t))|γ−1x(τ(t)))=0$

on an arbitrary time scale T with sup T = ∞, where n ≥ 2, γ > 0 is a constant, τ: TT with τ(t) ≤ t and $\underset{t\to \mathrm{\infty }}{lim}\tau \left(t\right)=\mathrm{\infty }$ and $Rk(t,x(t))=x(t),ifk=0,rk(t)Rk−1△(t,x(t)),if1≤k≤n−1,rn(t)|Rn−1△(t,x(t))|γ−1Rn−1△(t,x(t)),ifk=n,$

with rk(t) (1 ≤ kn) are positive rd-continuous functions. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

MSC 2010: Primary 34K11; 39A10; 39A99

Keywords: oscillation; dynamic equation; time scale

Project Supported by NNSF of China (11461003) and NSF of Guangxi (2014GXNSFBA118003)

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Accepted: 2014-01-09

Published Online: 2016-08-26

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 627–650, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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