Open Access
2011 Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales
H. A. Agwa, A. M. M. Khodier, Heba A. Hassan
Int. J. Differ. Equ. 2011(SI2): 1-15 (2011). DOI: 10.1155/2011/863801


In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation (p(t)(xΔ(t))γ)Δ+q(t)f(x(τ(t)))=0, on a time scale , where γ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous (rd-continuous) functions on 𝕋. Our results improve and extend some results established by Sun et al. 2009. Also our results unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our main results.


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H. A. Agwa. A. M. M. Khodier. Heba A. Hassan. "Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales." Int. J. Differ. Equ. 2011 (SI2) 1 - 15, 2011.


Received: 3 May 2011; Accepted: 6 June 2011; Published: 2011
First available in Project Euclid: 26 January 2017

zbMATH: 1239.34107
MathSciNet: MR2824915
Digital Object Identifier: 10.1155/2011/863801

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI2 • 2011
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