Classification and Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations

In this paper, we give a classification of non-oscillatory solutions of a second-order neutral delay difference equation of the form ∆(xn − cnxn−τ ) + f(n, xg1(n), . . . , xgm(n)) = 0 (n ≥ n0 ∈ N). Some existence results for each kind of non-oscillatory solutions are also established.