# The Palais-Smale condition on contact type energy levels for convex Lagrangian systems

@article{Contreras2003ThePC, title={The Palais-Smale condition on contact type energy levels for convex Lagrangian systems}, author={Gonzalo Contreras}, journal={Calculus of Variations and Partial Differential Equations}, year={2003}, volume={27}, pages={321-395} }

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 Mañé's critical value of the lift of the Lagrangian to the universal cover, cu(L), almost all energy levels have conjugate points.We in addition prove that if an energy level is of contact type, projects onto M and $$M\ne{\mathbb T}^2$$, then the free time action functional of L+k satisfies the Palais-Smale condition.

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