This article concerns the oscillation of second-order nonlinear dynamic equations. By using generalized Riccati transformations, Kiguradzetype and Belohorec-type oscillation theorems are obtained on an arbitrary time scale. Our results cover those for differential equations and difference equations, and provide new oscillation criteria for irregular time scales. Some examples are given to illus...

New oscillation criteria for certain fourth order nonlinear dynamic equations with nonlinear middle term are established. Mathematics subject classification (2010): 34K11, 39A10, 39A99, 34C10, 34C15, 34N05.

This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...