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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 253107, 18 pages
http://dx.doi.org/10.1155/2012/253107
Research Article

Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

Department of Mathematics, Faculty of Sciences, Erciyes University, 38039 Kayseri, Turkey

Received 6 March 2012; Accepted 22 March 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 M. Tamer Şenel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The oscillation of solutions of the second-order nonlinear dynamic equation ( 𝑟 ( 𝑡 ) ( 𝑥 Δ ( 𝑡 ) ) 𝛾 ) Δ + 𝑝 ( 𝑡 ) ( 𝑥 Δ ( 𝑡 ) ) 𝛾 + 𝑓 ( 𝑡 , 𝑥 ( 𝑔 ( 𝑡 ) ) ) = 0 , with damping on an arbitrary time scale 𝕋 , is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.