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


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