On a Class of Discrete Problems with the $p(k)$-Laplacian-Like Operators (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we consider a nonlinear discrete problem originatingfrom a capillary phenomena, involving the $p(k)$-Laplacian-like operators withmixed boundary condition. Under appropriate assumptions on the function $f$ and its primitive $F$ near zero and infinity, we investigate the existence andmultiplicity of nontrivial solutions by using variational methods and criticalpoint theory.