New oscillations criteria of delay partial difference equations

Consider the delay partial difference equation A(m+1,n) + A(m,n+1) - A(m,n) + Sigma(u)(i=1) P-i(m, n)A(m-ki, n-li) = 0, m, n is an element of N-0, where lim inf(m,n ->infinity) P-i(m, n) = p(i) is an element of [0, infinity), k(i), l(i), is an element of N-1, i = 1, 2,..., u. Sufficient conditions for the oscillation of all solutions of the above equation are established in the case when that the corresponding "limiting" equation A(m+1,n) + A(m,n+1) - A(m,n) + Sigma(u)(i=1) piA(m-ki,n-li) = 0, m, n is an element of N-0, admits non-oscillatory solutions. Oscillation criteria for nonlinear partial difference equation are also derived as applications.