Extensions of Ladas' oscillation theorem to polytopic difference equations

Abstract

We consider the difference equation where the coefficients bi are functions of the parameter vector p belonging to a convex polytope P in the parameter space. The purpose of this paper is to present general conditions for oscillation of all solutions of the difference equation for each p in P, which involve only the vertices of P. The oscillation property is established using Ladas theorem and testing positivity of vertex polynomials via the Modified Routh Array