Multiplicity of heteroclinic solutions for the discrete p(k)-Laplace Kirchhoff type equations with a parameter

In this paper, we prove the existence of at least one and of at least two nontrivial heteroclinic solutions for the discrete p(k)-Laplace Kirchhoff type equations depending on a parameter. The proof of our main result is based on a local minimum theorem for differentiable functionals due to Ricceri and on the mountain pass theorem of P. Pucci and J. Serrin.