Necessary and sufficient conditions for oscillation of solution of scalar difference equations (Q2289515)

Summary: 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 \(e^{\lambda n}\) 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.