Helmholtz's inverse problem of the discrete calculus of variations

Abstract

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.

This is a preprint of a paper whose final and definite form is published in Journal of Difference Equations and Applications