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

Abstract

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