Abstract
In this paper, we consider nonlinear partial difference equations of the form
Δ
n
hΔ
m
r (x
m,n − cx
m−k,n−l) + (−1)
h+r+1Pm,nƒ(x
m−τ,n−δ) = 0
, where
cϵ
R,
h,r,k,l ϵ
N
+, τ,δ ϵ
N, {
Pm,n}
m = m
0
∞,∞
, n = n
0
is 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 Knaster's fixed-point theorem.