MMN-4015
A new oscillation result for nonlinear differential equations with nonmonotone delay
Nurten Kilic; Özkan Öcalan;Abstract
In this paper, we investigate the oscillation of solutions of first order
nonlinear delay differential equation%
\begin{equation*}
x^{\prime }(t)+p(t)f(x(\tau (t)))=0,\text{ }t\geq t_{0},
\end{equation*}%
where the functions $p(t)$ and $\tau (t)$ are functions of nonnegative real
numbers, $\tau (t)$ is not necessarily monotone such that $\tau (t)\leq t$
for$\ t\geq t_{0},\ \lim_{t\rightarrow \infty }\tau (t)=\infty $ and $f\in C(%
\mathbb{R},\mathbb{R})$ and $xf(x)>0$ for $x\neq 0$ and we obtain a new
oscillation criterion for this equation. Finally, we present examples to
demonstrate the main result.
Vol. 24 (2023), No. 2, pp. 841-851
DOI: 10.18514/MMN.2023.4015