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# An oscillation criterion for first order linear delay differential equations

Published:1998-06-01
Printed: Jun 1998
• Ch. G. Philos
• Y. G. Sficas
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## Abstract

A new oscillation criterion is given for the delay differential equation $x'(t)+p(t)x \left(t-\tau(t)\right)=0$, where $p$, $\tau \in \C \left([0,\infty),[0,\infty)\right)$ and the function $T$ defined by $T(t)=t-\tau(t)$, $t\ge 0$ is increasing and such that $\lim_{t\to\infty}T(t)=\infty$. This criterion concerns the case where $\liminf_{t\to\infty} \int_{T(t)}^{t}p(s)\,ds\le \frac{1}{e}$.
 Keywords: Delay differential equation, oscillation
 MSC Classifications: 34K15 - unknown classification 34K15

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