Advances in Difference Equations
Volume 2009 (2009), Article ID 562329, 10 pages
doi:10.1155/2009/562329
Research Article

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

Tongxing Li,1 Zhenlai Han,1,2 Shurong Sun,1,3 and Dianwu Yang1

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 5 March 2009; Revised 24 June 2009; Accepted 24 August 2009

Academic Editor: Alberto Cabada

Copyright © 2009 Tongxing Li 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.

Abstract

We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation [x(t)+p(t)x(τ0(t))]ΔΔ+q1(t)x(τ1(t))−q2(t)x(τ2(t))=e(t) on a time scale 𝕋. To dwell upon the importance of our results, one interesting example is also included.