Oscillation criteria for higher-order neutral type difference equations

Authors

TURHAN KÖPRÜBAŞI
ZAFER ÜNAL
YAŞAR BOLAT

Abstract

In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form% \begin{equation} \Delta (r_{n}(\Delta ^{k-1}(y_{n}+p_{n}y_{\tau _{n}}))+q_{n}f(y_{\sigma _{n}})=0\text{, }n\geq n_{0}\text{,} \tag{0.1} \end{equation}% where $r_{n},p_{n},q_{n}\in \lbrack n_{0},\infty ),$ $r_{n}>0$, $q_{n}>0$; $% 0\leq p_{n}\leq p_{0}0$; $\tau _{\sigma }=\sigma _{\tau }$; $\frac{f(u)}{u}\geq m>0$ for $u\neq 0$. Moreover, we provide some examples to illustrate our main results.

DOI

10.3906/mat-1703-6

Keywords

Oscillation, oscillatory, difference equations

First Page

729

Last Page

738

Recommended Citation

KÖPRÜBAŞI, TURHAN; ÜNAL, ZAFER; and BOLAT, YAŞAR (2020) "Oscillation criteria for higher-order neutral type difference equations," Turkish Journal of Mathematics: Vol. 44: No. 3, Article 8. https://doi.org/10.3906/mat-1703-6
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/8