NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS

Abstract

<abstract> This paper is concerned with the oscillation of the first order linear delay differential equation $ x'(t)+q(t) x(\tau(t))=0 $, $ t\geq t_0 $, where $ q, \tau \in C([t_0,\infty),[0,\infty)) $, $ \tau(t)\leq t $, such that $ \underset{t \rightarrow \infty} {\lim} \tau(t)=\infty $. Several new oscillation criteria of iterative and non-iterative types are obtained. Two examples are presented to show the strength and applicability of these criteria over known ones. </abstract>