On homoclinic solutions for a class of fourth-order <i>ϕ</i> _c -Laplacian partial difference equations

The aim of this paper is to study the multiple nontrivial homoclinic solutions for a class of fourth-order nonlinear ϕc-Laplacian partial difference equations by exploiting the Mountain Pass Lemma and the Symmetric Mountain Pass Lemma. Our assumptions relax some known ones, and the results improve some relative existing references. To demonstrate the applications of our results, three practical examples are provided.