Existence of positive solutions for certain nonlinear partial difference equations

In this paper, we consider nonlinear partial difference equations of the form Delta(n)(h)Delta (r)(m) (x(m,n) - cx(m-k, n-l) ) + (-1)(h+r+1)p(m,n) f (x(m - r, n-sigma)) = 0, where c is an element of R, h, r, k, l is an element of N+, tau, sigma is an element of N, {p(m,n)} m = m(0), n = n(0) is a double sequence of real numbers and f is an element of C(R, R). We obtain sufficient conditions for the existence of positive solutions of this equation using Knaster's fixed-point theorem. (C) 2003 Elsevier Ltd. All rights reserved.