Oscillation of higher order systems of differential equations

In this paper, we provide necessary and sufficient conditions for theoscillation of every solution of the system of delay differential equations begin{equation*}x^{(m)}(t)+Px(t-tau )=0,,end{equation*}where $Pin mathbb{R}^{stimes s},$ $tau in mathbb{R}^{+}$ and $m$ is anodd positive integer. Furthermore, we proved sufficient conditions for theoscillation of every solution of the system of delay differential equations begin{equation*}x^{(m)}(t)+sum_{i=1}^{n}P_{i}x(t-tau _{i})=0,end{equation*}where $P_{i}in mathbb{R}^{stimes s},$ $tau _{i}in mathbb{R}^{+}$ for $%i=1,2,...,n$ and $m$ is an odd positive integer.