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

Contreras, Gonzalo
November 2006
Calculus of Variations & Partial Differential Equations;Nov2006, Vol. 27 Issue 3, p321
Academic Journal
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��'s critical value of the lift of the Lagrangian to the universal cover, c u ( 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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