  We prove that for a uniformly convex Lagrangian system L on a compact
manifold M, almost all energy levels contain a periodic orbit. We also prove
that below Ma ne's critical value of the lift of the Lagrangian to the
universal cover, almost all energy levels have conjugate points.
  We prove that if the energy level [E=k] is of contact type and M is not the
2-torus then the free time action functional of L+k satisfies the Palais-Smale
condition.
