Abstract and Applied Analysis

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

Quanwen Lin, Baoguo Jia, and Qiru Wang

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Abstract

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation ( r ( t ) [ x Δ ( t ) ] α ) Δ + p ( t ) x α ( 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 ) + c sin t x α ( t ) = cos t , where α = 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


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