In this paper, we study a class of bi-nonlocal fourth-order discrete problems involving p(k)-Laplacian operator in a finite dimensional Banach space. By using the variational method and the (S+) mapping theory, we investigate the existence and multi- plicity of nontrivial solutions, subject to the condition that the parameters are sufficiently large.

Bi-nonlocal problem, Kirchhoff type equation, Mixed boundary conditions, Mountain pass Theorem.