中文摘要：

研究了p-Laplace型差分方程△[φp（△y（t-1））]-q（t）φp（y（f））＋f（t,，y（t））=0的非平凡同宿轨的存在性，其中q（t）和f（t,y）没有任何周期性假设条件．首先建立了对应的变分框架；其次应用临界点理论得到非平凡同宿轨存在性的充分条件．将文献中P=2的情形推广到P≥2，改进了相应的结论．

英文摘要：

This paper mainly deals with the existence of nontrivial homoclinic orbit for the p-Laplacian differ- ence equations △[φp（△y（t-1））]-q（t）φp（y（f））＋f（t,,y（t））=0 without the periodicity assumptions on q （t） andf（t ,y）. The authors establish the corresponding variational framework. By using the critical point theory, they obtain a sufficient condition for the existence of nontrivial homoclinic orbit. The result generalizes those obtained in the references in the case p = 2.