## Abstract and Applied Analysis

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

#### Abstract

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation $(r(t)[{x}^{\Delta }(t){]}^{\alpha }{)}^{\Delta }+p(t){x}^{\alpha}(\sigma (t))=f(t)$ on a time scale $\mathbb{T}$ 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 $([{x}^{\prime }(t){]}^{\alpha }{)}^{\prime }+c\sin t{x}^{\alpha}(t)=\cos t$, where $\alpha =p/q$, $p$, $q$ are odd positive integers.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 294194, 10 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620758

Digital Object Identifier
doi:10.1155/2010/294194

Mathematical Reviews number (MathSciNet)
MR2680409

Zentralblatt MATH identifier
1205.34134

#### Citation

Lin, Quanwen; Jia, Baoguo; Wang, Qiru. Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales. Abstr. Appl. Anal. 2010 (2010), Article ID 294194, 10 pages. doi:10.1155/2010/294194. https://projecteuclid.org/euclid.aaa/1288620758