A SHARP OSCILLATION CRITERION FOR A DIFFERENCE EQUATION WITH CONSTANT DELAY

Benekas, Vasileios; Kashkynbayev, Ardak; Stavroulakis, Ioannis P.

dc.contributor.author	Benekas, Vasileios
dc.contributor.author	Kashkynbayev, Ardak
dc.contributor.author	Stavroulakis, Ioannis P.
dc.date.accessioned	2021-07-10T09:13:52Z
dc.date.available	2021-07-10T09:13:52Z
dc.date.issued	2020
dc.identifier.citation	Benekas, V., Kashkynbayev, A., & Stavroulakis, I. P. (2020). A sharp oscillation criterion for a difference equation with constant delay. Advances in Difference Equations, 2020(1). https://doi.org/10.1186/s13662-020-03016-x	en_US
dc.identifier.uri	http://nur.nu.edu.kz/handle/123456789/5556
dc.description.abstract	It is known that all solutions of the difference equation Δx(n)+p(n)x(n−k)=0,n≥0, where {p(n)}∞n=0 is a nonnegative sequence of reals and k is a natural number, oscillate if lim infn→∞∑n−1i=n−kp(i)>(kk+1)k+1. In the case that ∑n−1i=n−kp(i) is slowly varying at infinity, it is proved that the above result can be essentially improved by replacing the above condition with lim supn→∞∑n−1i=n−kp(i)>(kk+1)k+1. An example illustrating the applicability and importance of the result is presented.	en_US
dc.language.iso	en	en_US
dc.publisher	Advances in Difference Equations	en_US
dc.rights	Attribution-NonCommercial-ShareAlike 3.0 United States	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-sa/3.0/us/	*
dc.subject	Type of access: Open Access	en_US
dc.subject	equation	en_US
dc.title	A SHARP OSCILLATION CRITERION FOR A DIFFERENCE EQUATION WITH CONSTANT DELAY	en_US
dc.type	Article	en_US
workflow.import.source	science