Asymptotic behavior and oscillation of delay partial difference equations with positive and negative coefficients

摘要

We obtain sufficient conditions for the oscillation of all solutions of the linear partial difference equations with positive and negative coefficients of the form A(m-1,n) + A(m,n-1) - A(mn) + pA(m+k n+l) - qA(m+k') (n+l') = 0, and A(m-1,n) + A(m,n-1) - A(mh) + P(mn)A(m+k n+l) - q(mn)A(m+k') (n+l') = 0, where m, n = 0, 1, . . . , and k, k', l', l are nonnegative integers p, q is an element of (0, infinity), and coefficients {q(mn)} and {P-mn} are sequences of nonnegative real numbers. In this paper A(mn) = A(m,n). [References: 11]