Existence of nonoscillatory solutions to third order nonlinear neutral difference equations

Abstract

The authors consider the third order neutral delay difference equation with positive and negative coefficients ?(an?(bn?(xn + pxn-m)))+pnf(xn-k)- qn1(xn-l) = 0, n ? n0, and give some new sufficient conditions for the existence of nonoscillatory solutions. Banach?s fixed point theorem plays a major role in the proofs. Examples are provided to illustrate their main results.