The oscillatory properties of solutions to the $n$th order delay differential equations $L_{n}y\left(t\right)+p\left(t\right)y\left(\tau \left(t\right)\right)=0,$where $L_n$ is a disconjugate strongly noncanonical differential operator, $p\left(t\right)>0$, $\tau \left(t\right)\le t$, and ${lim}_{t\to \infty }\tau \left(t\right)=\infty$, are studied. The main idea is to show that, unlike Trench original, rather theoretical result, simple closed formulas appearing in a uniquely determined canonical representation of $L_n$ are possible, under one (mild) additional condition. As a consequence, new oscillation theorems for strongly noncanonical higher-order equations are formulated. Moreover, our results generalize even several ones obtained for $n=3,4$.

中文翻译：

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振荡 $ñ$三阶强非规范时滞微分方程

解的振荡性质 $ñ$一阶时滞微分方程 ${\mathrm{大号}}_{ñ}ÿ（Ť）+p（Ť）ÿ（\tau （Ť））=0，$哪里 ${\mathrm{大号}}_{ñ}$ 是一个非强共轭非规范微分算子， $p（Ť）>0$， $\tau （Ť）\le Ť$和 ${林}_{Ť\to \infty }\tau （Ť）=\infty$，正在研究中。主要思想是表明，与Trench的原始结果（而不是理论上的结果）不同，简单的闭合公式以唯一确定的典范表示形式出现${\mathrm{大号}}_{ñ}$在一个（轻微）附加条件下是可能的。结果，为强非规范高阶方程制定了新的振动定理。此外，我们的结果可以概括为$ñ=3，4$。