Abstract and Applied Analysis
Volume 2010 (2010), Article ID 428963, 16 pages
doi:10.1155/2010/428963
Research Article

Nonoscillatory Solutions for Higher-Order Neutral Dynamic Equations on Time Scales

Taixiang Sun,1 Hongjian Xi,2 Xiaofeng Peng,1 and Weiyong Yu1

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China

Received 16 May 2010; Revised 4 July 2010; Accepted 16 July 2010

Academic Editor: D. Anderson

Copyright © 2010 Taixiang Sun 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 study the higher-order neutral dynamic equation {a(t)[(x(t)−p(t)x(τ(t)))Δm]α}Δ+f(t,x(δ(t)))=0 for t∈[t0,∞)T and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.