Variational Approaches for Lagrangian Discrete Nonlinear Systems

Abstract

In this paper, we study the multiple solutions for Lagrangian systems of discrete second-order boundary value systems involving the discrete p-Laplacian operator. The technical approaches are based on a local minimum theorem for differentiable functionals in a finite dimensional space and variational methods due to Bonanno. The existence of at least one solution, as well as three solutions for the given system are discussed and some examples and remarks have also been given to illustrate the main results.