Advances in Difference Equations
Volume 2010 (2010), Article ID 586312, 23 pages
Research Article

Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
3Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA

Received 14 September 2009; Revised 28 November 2009; Accepted 10 December 2009

Academic Editor: Leonid Berezansky

Copyright © 2010 Zhenlai Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations (r(t)(x(t)a(t)x(τ(t)))ΔΔ)Δ+p(t)xγ(δ(t))=0 on a time scale 𝕋, where γ>0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on 𝕋. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.