Nonexistence of unbounded nonoscillatory solutions of partial difference equations (Q1380365)

The authors develop criteria for the nonexistence of eventually positive (negative) and nondecreasing (nonincreasing) solutions of the partial difference equation \[ \nabla_m \nabla_n y(m,n)+ P\bigl(m,n,y (m+k, n+l)\bigr) =Q \bigl(m,n, y(m+k,n-l) \bigr) \] and \[ \nabla_m \nabla_n y(m,n)+ \sum^\tau_{i=1} P_i\bigl(m,n,y (m+k_i, n+l_i)\bigr)= \sum^\tau_{i= 1} Q_i \bigl(m,n,y (m+k_i,n+l_i) \bigr). \] Several examples which dwell upon the importance of the results are also included.