Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Abstract

In this article, we analyze the first order linear delay differential equation
 \begin{equation*}
 x^{\prime }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\geq t_{0},
 \end{equation*}
 where $p,$ $\tau \in C\left( [t_{0},\infty ),\mathbb{R}^{+}\right) $ and $%
 \tau (t)\leq t,\ \lim_{t\rightarrow \infty }\tau (t)=\infty $. Under the assumption that $\tau (t)$ is not necessarily monotone, we obtain new sufficient criterion for the oscillatory solutions of this equation. We also give an example illustrating the result.