Oscillation of higher-order difference equations

Abstract We shall establish sufficient conditions for the oscillation of all solutions of the even-order difference equations of the form ▵ m x n +P n ▵ m−1 x n +F(n,x n−g , ▵x n−h )=0, m is even, by comparing it with certain difference equations of lower order whose oscillatory character is known. The obtained results can be applied to the difference equation ▵ m x n +P n ▵ m−1 x n +q n |x n−g | λ |▵x n−h z.sfnc;u sgc x n−g =0, m is even, where λ > 0 and μ ≥ 0 are real constants.