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Abstract and Applied Analysis
Volume 2010 (2010), Article ID 294194, 10 pages
http://dx.doi.org/10.1155/2010/294194
Research Article

Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales

Quanwen Lin,1 Baoguo Jia,2 and Qiru Wang2

1Department of Mathematics, Maoming University, Maoming 525000, China
2Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received 14 March 2010; Revised 19 June 2010; Accepted 12 July 2010

Academic Editor: Allan C. Peterson

Copyright © 2010 Quanwen Lin 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 will establish a new interval oscillation criterion for second-order half-linear dynamic equation (r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cos⁡t, where α=p/q, p, q are odd positive integers.