Linearized comparison theorems for a nonlinear delay 2D discrete dynamic systems

This paper deals with a class of a nonlinear delay 2D discrete dynamical systems of the form A_m+1,n+A_m,n+1-A_mn+Σ_i=1 ^κPi(m,n)f_i(A_m+σi,n+A _m,n+σi)=0, (E). We show that if a positive solution exists, then a related minorant equation has a positive solution as well. Similar results for a dual equation are also obtained. In fact, we remark further that equation (E) may also be regarded as a discrete analog of partial differential equations of the form ∂u/∂x+∂u/∂y-u(x,y)+Σ_i=1^κ Pi(x,y)f_i(u(x+σ_i,y)+u(x,y+σ _i))=0. Therefore, qualitative of (E) may yield useful information for this companion partial differential equation