In this paper, we investigate the existence and multiplicity of so- lutions 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 tech- niques, particularly the mountain pass theorem of A. Ambrosetti and P.H. Rabinowitz and the (S+) mapping theory.

Kirchhoff type equation, nonlocal discrete problem, p(k)-capillarity differential operator, boundary value problem, multiple solutions, mountain pass theorem, (S+) mapping theory