Existence of bounded positive solutions for a system of difference equations

Abstract

This paper deals with the second order nonlinear neutral delay system of difference equationsΔ[anΔ(xn+bnxn-τ)]+f(n,xh1n,…,xhkn,yw1n,…,ywkn)=cn,n⩾n0,Δ[pnΔ(yn+qnyn-σ)]+g(n,xs1n,…,xskn,yt1n,…,ytkn)=rn,n⩾n0.By virtue of the Banach fixed point theorem and some natural modifications of the techniques in the literature, we prove the existence results of uncountably many bounded positive solutions for the system of difference equations. Seven examples are constructed to explain the main results presented in this paper.