Some discrete nonlinear inequalities and applications to boundary value problems for difference equations

In this paper, we establish some new discrete Gronwall-Bellman-Ou-Iang type inequalities over 2-dimensional lattices. These, on one hand, generalize some existing results in the literature and on the other hand, provide a handy tool for the study of qualitative properties of solutions of difference equations. We illustrate this by applying these new results to certain boundary value problem for difference equations.