Multiplicity results for discrete partial mean curvature problems

In this article we continue the study of nonlinear discrete Dirichlet boundary value problems driven by mean curvature operators. By using a consequence of the local minimum theorem due Bonanno and mountain pass theorem, we will obtain a new multiplicity results of the solutions for a nonlinear discrete Dirichlet boundary value problems driven by \(\phi _c\) ${\varphi }_c$ -Laplacian operator which have applications in the dynamic model of combustible gases, the capillarity problem in hydrodynamics, and flux-limited diffusion phenomenon, under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Also, we establish the existence of third solution for our problem, by mountain pass theorem given by Pucci and Serrin.