### Oscillation of Nonautonomous Second Order Neutral Delay Dynamic Equations on Time Scales

*H. A. Agwo*

#### Abstract

In this paper, we establish some new oscillation criteria for nonautonomous second order neutral delay dynamic equation with several delays

\begin{equation*}

(x(t)-r(t)x(\tau (t)))^{\triangle \triangle }+H(t,x(h(t)))+G(t,x(g(t)))=0 {\normalsize ,}

\end{equation*}

on a time scale $\mathbb{T}$. The results not only can be applied on neutral differential equations when $\mathbb{T}=\mathbb{R}$, neutral delay difference equations when $\mathbb{T=N}$ and for neutral delay $q-$ difference equations when $\mathbb{T=}q^{\mathbb{N}}$ for $q>1$, but also improved most previous results.

\begin{equation*}

(x(t)-r(t)x(\tau (t)))^{\triangle \triangle }+H(t,x(h(t)))+G(t,x(g(t)))=0 {\normalsize ,}

\end{equation*}

on a time scale $\mathbb{T}$. The results not only can be applied on neutral differential equations when $\mathbb{T}=\mathbb{R}$, neutral delay difference equations when $\mathbb{T=N}$ and for neutral delay $q-$ difference equations when $\mathbb{T=}q^{\mathbb{N}}$ for $q>1$, but also improved most previous results.

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