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International Journal of Differential Equations
Volume 2011 (2011), Article ID 863801, 15 pages
doi:10.1155/2011/863801
Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Received 3 May 2011; Accepted 6 June 2011
Academic Editor: Elena Braverman
Copyright © 2011 H. A. Agwa et al. 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
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 , on a time scale where is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous (rd-continuous) functions on . 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.