2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57022The purpose of this paper is to announce some new results on the structure of the higher order Euler-Lagrange mapping of the multiple-integral variational calculus on fibered manifolds,namely a description of its kernel and its image,and an explicit characterization of the conditions under which a system of partial differential equations (of arbitrary order)is a system of the Euler--Lagrange equations.6 pagesMathematical Physicstext