The fixed energy problem for a class of nonconvex singular Hamiltonian systems

Tanaka, Kazunaga; Séré, Eric; Carminati, Carlo

Tanaka, Kazunaga; Séré, Eric; Carminati, Carlo (2006), The fixed energy problem for a class of nonconvex singular Hamiltonian systems, Journal of Differential Equations, 230, 1, p. 362-377. http://dx.doi.org/10.1016/j.jde.2006.01.021

Type

Article accepté pour publication ou publié

Date

2006

Nom de la revue

Journal of Differential Equations

Volume

230

Numéro

Éditeur

Elsevier

Pages

362-377

Résumé (EN)

We consider a noncompact hypersurface H in R2N which is the energy level of a singular Hamiltonian of “strong force” type. Under global geometric assumptions on H, we prove that it carries a closed characteristic, as a consequence of a result by Hofer and Viterbo on the Weinstein conjecture in cotangent bundles of compact manifolds. Our theorem contains, as particular cases, earlier results on the fixed energy problem for singular Lagrangian systems of strong force type.

Mots-clés

Hamiltonian system; Hypersurface of contact type; Closed characteristic; Cotangent bundle; Critical point theory; Variational methods; Singular potential; Strong force; Weinstein conjecture