Nonexistence of unbounded nonoscillatory solutions of partial difference equations

Abstract

We develop criteria for the nonexistence of eventually positive (negative) and nondecreasing (nonincreasing) solutions of the partial difference equation ∇m∇ny(m, n) + P(m, n, y(m + k, n + l)) = Q(m, n, y(m + k, n + l)) and ∇m∇ny(m, n) + ∑τ i=1 Pi(m, n, y(m + ki, n + li)) = ∑τ i=1 Qi(m, n, y(m + ki, n + li)). Several examples which dwell upon the importance of our results are also included. © 1997 Academic Press.