中文摘要：

考虑含超前与滞后量的2n阶p-Laplace差分方程边值问题.首先,引入一个合适的希尔伯特空间并在此空间上定义一个泛函使其临界点对应于边值问题的解.然后,建立几个不等式并利用临界点理论获得泛函临界点的存在性.由此得到边值问题解的存在性的一些充分条件.本文结果推广和改进了最近文献的相关结论.

英文摘要：

In this paper , we consider the boundary value problems for a 2n-order p-Laplacian difference equa-tion containing both advance and retardation .First, we introduce a suitable Hilbert space and define a function-al on this space such that the critical points of the functional correspond to the solutions of the boundary value problem.Then, by several established inequalities and critical point theory , we obtain the existence of critical points of the functional .Thus, sufficient conditions of the existence of solutions of the boundary value problems are obtained .Our results generalize and improve some recent ones .