Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Year 2021, Volume: 13 Issue: 2, 310 - 317, 31.12.2021

Nurten Kılıç

https://doi.org/10.47000/tjmcs.893395

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.

Keywords

Delay equation, nonmonotone argument, oscillatory solution, nonoscillatory solution

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