Nonoscillation and oscillation criteria for class of higher - order difference equations involving generalized difference operator

Abstract

Summary: In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the form \[ \Delta_a^k(p_n\Delta_a^2y_n)=f(n,y_n,\Delta_ay_n,\Delta_a^2y_n,\dots,\Delta_a^{k+1}y_n), \] where \(\Delta_a\) is generalized difference operator which is defined as \(\Delta_ay_n=y_{n+1}-ay_n\), \(a\neq{0}\).