In the present paper the oscillatory properties of the solutions of the equation (The equation is abbreviated) are investigated where n ≥ 1, L is an operator of the difference type, I_t⊂R, K:D_K→R, D_K⊆R^3, x:[αx, ∞]→R. Under natural conditions imposed on L,I_t and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t→∞.