Linearized oscillation theorems for certain nonlinear delay partial difference equations

This paper is concerned with the nonlinear delay partial difference equation Am+1,n+Am,n+1−Am,n+Pm,nf(Am−k,n−1)=0, where k and l are nonnegative integers and m, N = 0, 1, …. Some linearized oscillation theorems for this equation are obtained, i.e., we will prove that under some conditions on f, this equation has the same oscillatory character as an associated linear equation. An existence result for positive solutions of this equation is obtained also.