Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales. (29th June 2009)

• Record Type: Journal Article
• Authors: Han, Zhenlai; Li, Tongxing; Sun, Shurong; Zhang, Chenghui
• Other Names: Cabada Alberto Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-06-29
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/756171
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations( r ( t ) ( x Δ ( t ) ) γ ) Δ + p ( t ) f ( x ( τ ( t ) ) ) = 0 on a time scale𝕋 ; hereγ > 0 is a quotient of odd positive integers withr andp real-valued positive rd-continuous functions defined on𝕋 . Our results not only extend some results established by Hassan in 2008 but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.