Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales. (21st March 2013)

• Record Type: Journal Article
• Authors: Sun, Yibing; Han, Zhenlai; Sun, Shurong; Zhang, Chao
• Other Names: Wong Patricia J. Y. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/359240
• Languages: English
• ISSNs: 1085-3375

Abstract

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 scale𝕋 which is unbounded, whereα 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.