Abstract and Applied Analysis

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

Yibing Sun, Zhenlai Han, Shurong Sun, and Chao Zhang

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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 Δ ( t ) ) Δ + p ( t ) x Δ σ ( t ) + q ( t ) ( x σ ( t ) ) α = F ( t , x σ ( t ) ) on a time scale 𝕋 which is unbounded, where α 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

Permanent link to this document
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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