Abstract
By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations , , where , and the time scale interval is . Our results in this paper not only extend the results given by Agarwal et al. (2005) but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.
Highlights
The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D
A time scale T is an arbitrary closed subset of the reals, and the cases when this time scale is equal to the reals or to the integers represent the classical theories of differential and of difference equations
To the best of our knowledge, there are no results regarding the oscillation of the solutions of the following second-order nonlinear neutral delay dynamic equations on time scales up to now: r t xΔ t γ−1xΔ t Δ q1 t y δ1 t α−1y δ1 t 1.7
Summary
The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D.
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