  The basic aim is to extend some results and concepts of non-autonomous second
order differential systems with convex potentials to the new context of
multi-time Poisson-gradient PDE systems with convex potential. In this sense,
we prove that minimizers of a suitable action functional are multiple
periodical solutions of a Dirichlet problem associated to the Euler-Lagrange
equations. Automatically, these are solutions of the associated multi-time
Hamiltonian equations.
