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

摘要

In this paper, necessary and sufficient conditions for the existence and classification of positive solutions of the higher-order neutral difference equationΔrnΔkxn−∑i=1mpnixn−τi+f(n,xn−σ1,…,xn−σl)=0are obtained, where rn>0, pni⩾0, i=1,2,…,m, and f(n,s1,…,sl) is continuous with respect to n and sj, j=1,…,l.