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.
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 *