Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation ΔnΔm(xm,n+am,nxm−k,n−l)+f(m,n,xm−τ,n−σ)=bm,n,m≥m0,n≥n0. Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation. Three nontrivial examples are given to illustrate the advantages of our results.