Classifications and existence of positive solutions of higher-order nonlinear neutral difference equations

Abstract

In this paper, necessary and sufficient conditions for the existence and classification of positive solutions of the higher-order neutral difference equation Δ r n Δ k x n−∑ i=1 mp n ix n−τ i +f(n,x n−σ 1 ,…,x n−σ l )=0 are obtained, where r n >0, p n i ⩾0, i=1,2,…, m, and f( n, s 1,…, s l ) is continuous with respect to n and s j , j=1,…, l.