Existence of a nonoscillatory solution of a second-order linear neutral difference equation

Abstract

Consider the neutral delay difference equation with positive and negative coefficients, Δ 2 ( x n + p x n − m ) + p n x n − k − q n x n − l = 0 , where p ∈ R and m , k , l ∈ N and p n , q n ∈ R + , n ≥ n 0 ∈ N . Some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of ∑ ∞ i p i < ∞ , ∑ ∞ i q i < ∞ are obtained.