Title: Necessary and sufficient conditions for oscillation of solution of scalar difference equations

Authors: Yutaka Shoukaku

Addresses: Faculty of Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan

Abstract: The purpose of this paper is to derive necessary and sufficient conditions for the oscillation of all solutions of the difference equation. In this paper, by letting eλn be a solution of the difference equation, we obtain a fundamental proof of the result that every solution of the difference equation oscillates if and only if the characteristic equation has no real root.

Keywords: difference equations; necessary and sufficient condition; oscillation.

DOI: 10.1504/IJDSDE.2017.086666

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.3, pp.229 - 239

Received: 04 Aug 2016
Accepted: 25 Nov 2016

Published online: 08 Sep 2017 *

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