Existence of positive solutions for certain nonlinear partial difference equations (Q597486)

The authors study the nonlinear partial difference equations of the form \[ \Delta_n^h\Delta_m^r(x_{m,n}-cx_{m-k,n-l})+(-1)^{h+r+1}p_{m,n}f(x_{m-\tau,n-\sigma})=0,\tag{E} \] where \(c\in \mathbb{R},\) \(h,r,k,l\in \mathbb{N}^+,\) \(\tau,\sigma\in \mathbb{N},\) \(\{p_{m,n}\}_{m=m_0,n=n_0}^{\infty,\infty}\) is a double sequence of real numbers and \(f\in C(\mathbb{R},\mathbb{R})\). By using Knaster's fixed point theorem, the authors obtain some sufficient conditions for the existence of positive solutions of the equation (E).