## Abstract and Applied Analysis

### Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales

#### Abstract

By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form $(r(t){x}^{\mathrm{\Delta }}(t){)}^{\mathrm{\Delta }}+p(t){x}^{\mathrm{\Delta }\sigma }(t)+q(t)({x}^{\sigma }(t){)}^{\alpha }=F(t,{x}^{\sigma }(t))$ on a time scale $\mathrm{\Bbb T}$ which is unbounded, where $\alpha$ is a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 359240, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393450067

Digital Object Identifier
doi:10.1155/2013/359240

Mathematical Reviews number (MathSciNet)
MR3035369

Zentralblatt MATH identifier
1279.34108

#### Citation

Sun, Yibing; Han, Zhenlai; Sun, Shurong; Zhang, Chao. Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 359240, 11 pages. doi:10.1155/2013/359240. https://projecteuclid.org/euclid.aaa/1393450067

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