On a Class of Discrete Problems with the $p(k)$-Laplacian-Like Operators

Abstract

In this paper, we consider a nonlinear discrete problem originating from a capillary phenomena, involving the $p(k)$-Laplacian-like operators with mixed boundary condition. Under appropriate assumptions on the function $f$ and its primitive $F$ near zero and infinity, we investigate the existence and multiplicity of nontrivial solutions by using variational methods and critical point theory.