The Palais-Smale condition on contact type energy levels for convex Lagrangian systems |
| |
Authors: | Gonzalo Contreras |
| |
Affiliation: | (1) CIMAT, A.P. 402, 36.000 Guanajuato, Gto., México |
| |
Abstract: | 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, 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 $Mne{mathbb T}^2We 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?é'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 , then the free time action functional of L+k satisfies the Palais-Smale condition.Partially supported by Conacyt, Mexico, grant 36496-E. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|