Corrigendum to "Oscillation behavior of third-order neutral Emden-Fowler delay xdynamic equations on time scales" [Adv. Difference Equ., 2010, 1-23 (2010)]

Ji Tao, Tang Shuhong, Li, Li Tongxing

Description

In this article, we revise results obtained by Han et al. Mathematics Subject Classification 2000: 34K11; 39A10. In this article, we revise results obtained by Han et al. Mathematics Subject Classification 2000: 34K11; 39A10.

Sujets

• Oscillation
• Time scale

Informations

• Publié par: biomed
• Publié le: 01 janvier 2012
• Nombre de lectures: 9
• Langue: English

Extrait

Jiet al.Advances in Difference Equations2012,2012:57 http://www.advancesindifferenceequations.com/content/2012/1/57

R E S E A R C HOpen Access Corrigendum to“Oscillation behavior of third order neutral EmdenFowler delay xdynamic equations on time scales”[Adv. Difference Equ., 2010, 123 (2010)] 1 12,3* Tao Ji , Shuhong Tangand Tongxing Li

* Correspondence: [e-mail] 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China Full list of author information is available at the end of the article

Abstract In this article, we revise results obtained by Han et al. Mathematics Subject Classification 2000:34K11; 39A10. Keywords:oscillation, thirdorder, neutral dynamic equation, time scale

1. Introduction EmdenFowler type dynamic equations have some applications in the real world; see the background details introduced by Hilger [1]. Hence [2] studied a class of third order Emden Fowler neutral dynamic equations  2  γ r(t)(x(t)−a(t)x(τ(t))) +p(t)x(δ(t)) = (1:1)

on a time scalewith sup = , where the authors assume the following hypoth eses hold.

(A 1 )g>0 is the quotient of odd positive integers; (A 2 )randpare positive realvalued rdcontinuous functions defined onsuch Δ thatr(t)≥0; (A 3 )ais a positive realvalued rdcontinuous function defined onsuch that 0< a (t)≤a 0 <1 and lim t®∞ a(t) =a 1 ; (A 4 ) the functions τT→ and δT→T are rdcontinuous functions such that τ(t)≤t,δ(t)≤t, and lim t®∞ τ(t) = lim t®∞ δ(t) =∞.

A time scaleis an arbitrary nonempty closed subset of the real numbersℝ. Since we are interested in oscillatory behavior, we suppose that the time scale under consid eration is not bounded above and is a time scale interval of the form [ [ t 0 ,∞ ) :=t 0 ,∞ ) ∩ . For some concepts related to the notion of time scales; see [3]. Regarding the oscillation properties of (1.1) witha(t) = 0, Saker [47] established some types of criteria, e.g., HilleNeharitype and Philostype.

© 2012 Ji et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.