  Multiplicity results for solutions of various boundary value problems are
known for dynamical systems on compact configuration manifolds, given by
Lagrangians or Hamiltonians which have quadratic growth in the velocities or in
the momenta. Such results are based on the richness of the topology of the
space of curves satisfying the given boundary conditions. In this note we show
how these results can be extended to the classical setting of Tonelli
Lagrangians (Lagrangians which are $C^2$-convex and superlinear in the
velocities), or to Hamiltonians which are superlinear in the momenta and have a
coercive action integrand.
