Results on homoclinic solutions of a partial difference equation involving the mean curvature operator

By variational technique coupled with the mountain pass lemma and fountain theorem, we investigate a second-order partial difference equation involving the mean curvature operator in the present paper. We establish a number of criteria to guarantee the existence of multiple nontrivial homoclinic solutions. Our results generalize and improve some known ones. Additionally, two examples are provided to demonstrate applications of our obtained results.