Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 389109, 21 pages doi:10.1155/2010/389109 Research Article Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations M. ¨ Unal 1 and A. Zafer 2 1 Department of Software Engineering, Bahc¸es¸ehir University, Bes¸iktas¸, 34538 Istanbul, Turkey 2 Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey Correspondence should be addressed to M. ¨ Unal, munal@bahcesehir.edu.tr Received 19 January 2010; Accepted 20 March 2010 Academic Editor: Josef Diblik Copyright q 2010 M. ¨ Unal and A. Zafer. 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. New oscillation criteria are established for second-order mixed-nonlinear delay dynamic equations on time scales by utilizing an interval averaging technique. No restriction is imposed on the coefficient functions and the forcing term to be nonnegative. 1. Introduction In this paper we are concerned with oscillatory behavior of the second-order nonlinear delay dynamic equation of the form  r tx Δ t  Δ  p 0 txτ 0 t  n  i1 p i t|xτ i t| α i -1 xτ i t  et, t ≥ t 0 1.1 on an arbitrary time scale T, where α 1 >α 2 > ··· >α m > 1 >α m1 > ··· >α n > 0, n>m ≥ 1; 1.2 the functions r , p i , e: T → R are right-dense continuous with r> 0 nondecreasing; the delay functions τ i : T → T are nondecreasing right-dense continuous and satisfy τ i t ≤ t for t ∈ T with τ i t →∞ as t →∞. We assume that the time scale T is unbounded above, that is, sup T  ∞ and define the time scale interval t 0 , ∞ T by t 0 , ∞ T :t 0 , ∞ ∩ T. It is also assumed that the reader is already familiar with the time scale calculus. A comprehensive treatment of calculus on time scales can be found in 1–3.