Oscillation of second-order nonlinear neutral delay dynamic equations on time scales

In this paper, some sufficient conditions for oscillation of the second-order nonlinear neutral delay dynamic equation (r(t)([y(t)+ p(t)y(t − )] ) ) + f (t, y(t − ))= 0, on a time scale T are established; here 1 is an odd positive integer with r(t) and p(t) are rd-continuous functions defined on T. Our results as a special case when T = R and T = N, involve and improve some well-known oscillation results for second-order neutral delay differential and difference equations. When T= hN and T= q = {t : t = q, k ∈ N, q > 1}, i.e., for generalized neutral delay difference and q-neutral delay difference equations our results are essentially new and also can be applied on different types of time scales, e.g., T = N2 = {t2 : t ∈ N} and T= Tn = {tn: n ∈ N0} where {tn} is the set of harmonic numbers. Some examples illustrating our main results are given. © 2005 Elsevier B.V. All rights reserved. MSC: 34K11; 39A10; 39A99 (34A99, 34C10, 39A11)