Existence of positive solutions for certain nonlinear partial difference equations

In this paper, we consider nonlinear partial difference equations of the form ΔnhΔmr (xm,n − cxm−k,n−l) + (−1)h+r+1Pm,nƒ(xm−τ,n−δ) = 0, where cϵR, h,r,k,l ϵ N+, τ,δ ϵ N, {Pm,n} m = m0∞,∞, n = n0is a double sequence of real numbers and ƒ ϵ C(R, R). We obtain sufficient conditions for the existence of positive solutions of this equation using Knasterʹs fixed-point theorem.