Calculus of Variations and Geometric Measure Theory

A. Abbondandolo - A. Figalli

High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces

created by figalli on 19 Oct 2006
modified on 20 Dec 2006


Accepted Paper

Inserted: 19 oct 2006
Last Updated: 20 dec 2006

Journal: J. Differential Equations
Year: 2006


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.

Keywords: Lagrangian systems, Hamiltonian systems, multiplicity results, Lagrangian boundary condition