Nonlocal discrete problem involving the anisotropic p(k)-capillarity differential operator

In this paper, we investigate the existence and multiplicity of solutions for a class of nonlocal discrete problems governed by a p(k)-capillarity differential operator in a T-dimensional Banach space. Our technical approach is based on a minimization method combined with adequate variational techniques, particularly the mountain pass theorem of A. Ambrosetti and P.H. Rabinowitz and the (S_+) mapping theory.