Nonoscillation criteria for discrete hill equation

In this work we recover the Discrete Hill's equation introduced by Chulaevsky in 1989 [11] and give it a graphical interpretation of parametric stability [12] i.e. discrete Arnold tongues. We give the nonoscillatory criteria for discrete Hill's equation and proved that all the nonoscillatory solution of the discrete Hill's equation fall into the 0-th Arnold tongue.