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International Journal of Differential Equations
Volume 2016, Article ID 3298289, 12 pages
http://dx.doi.org/10.1155/2016/3298289
Research Article

Interval Oscillation Criteria for Forced Second-Order Nonlinear Delay Dynamic Equations with Damping and Oscillatory Potential on Time Scales

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt

Received 14 April 2016; Accepted 28 June 2016

Academic Editor: Said R. Grace

Copyright © 2016 Hassan 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

We are concerned with the interval oscillation of general type of forced second-order nonlinear dynamic equation with oscillatory potential of the form , on a time scale . We will use a unified approach on time scales and employ the Riccati technique to establish some oscillation criteria for this type of equations. Our results are more general and extend the oscillation criteria of Erbe et al. (2010). Also our results unify the oscillation of the forced second-order nonlinear delay differential equation and the forced second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our results.