Oscillation criteria for the second-order neutral advanced dynamic equations on time scales

Abstract

In this paper, we consider the oscillation of second-order neutral advanced dynamic equations on time scales of the form ${\left(r\left(t\right){\left(z^{\Delta }\left(t\right)\right)}^{\alpha }\right)}^{\Delta }+q\left(t\right)f\left(y\left(m\left(t\right)\right)\right)=0,$ where $z\left(t\right)=y\left(t\right)+p\left(t\right)y\left(\tau \left(t\right)\right)$ and $m\left(t\right)\ge t$. We consider two cases of $\tau \left(t\right)\ge t$ and $\tau \left(t\right)\le t$, respectively. Some new oscillatory results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second-order equations to the oscillation of the first-order equations.