Perturbed Kirchhoff-type p-Laplacian discrete problems

The present paper is an attempt to the study of multiplicity results of solutions for a class of perturbed p-Laplacian discrete problems of Kirchhoff-type. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for the problems. Moreover, assuming sign conditions on the nonlinear terms, we will prove that the solutions are non-negative. Finally, by presenting two examples, we will ensure the applicability of our results.