Abstract
In this paper, we give a classification of non-oscillatory solutions of a second-order neutral delay difference equation of the form $$\Delta^2(x_n – c_nx_{n–\tau}) + f (n, x_{g_1(n)},..., x_{g_m(n)}) = 0 (n ≥ n_0 \in \mathbb N).$$ Some existence results for each kind of non-oscillatory solutions are also established.