(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
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.