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Journal of Applied Mathematics and Computing

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03.11.2021 | Original Research

Iterative oscillation criteria for first-order difference equations with non-monotone advanced arguments

verfasst von: Emad R. Attia, George E. Chatzarakis

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 5/2022

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Abstract

Consider the first-order linear advanced difference equation of the form

$$\begin{aligned} \nabla x(n)-q(n)x(\sigma (n))=0, \qquad n\in {\mathbb {N}}, \end{aligned}$$

where $(q(n))_{n\ge 1}$ is a sequence of nonnegative real numbers and $(\sigma (n))_{n\ge 1}$ is a sequence of integers such that $\sigma (n)\ge n+1,$ for all $n\in {\mathbb {N}}$. Based on an iterative procedure, new oscillation criteria, involving $\lim \sup $, are established in the case of non-monotone advanced argument. Our conditions essentially improve several known results in the literature. Examples, numerically solved in Maple software, are also given to illustrate the applicability and strength of the obtained conditions over known ones.

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Titel: Iterative oscillation criteria for first-order difference equations with non-monotone advanced arguments
verfasst von: Emad R. Attia
George E. Chatzarakis
Publikationsdatum: 03.11.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 5/2022
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01648-0

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