NEW OSCILLATIONS CRITERIA OF DELAY PARTIAL DIFFERENCE EQUATIONS

Consider the delay partial difference equation Am+1,n + Am,n+1 − Am,n + Xu i=1 Pi(m, n)Am−ki,n−li = 0, m, n ∈ N0, where lim infm,n→∞ Pi(m, n) = pi ∈ [0, ∞), ki , li ∈ N1, 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 Am+1,n + Am,n+1 − Am,n + Xu i=1 piAm−ki,n−li = 0, m, n ∈ N0, admits non-oscillatory solutions. Oscillation criteria for nonlinear partial difference equation are also derived as applications.