TY - JOUR
T1 - The fixed energy problem for a class of nonconvex singular Hamiltonian systems
AU - Carminati, C.
AU - Séré, É
AU - Tanaka, K.
PY - 2006/11/1
Y1 - 2006/11/1
N2 - We consider a noncompact hypersurface H in R2 N 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.
AB - We consider a noncompact hypersurface H in R2 N 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.
KW - Closed characteristic
KW - Cotangent bundle
KW - Critical point theory
KW - Hamiltonian system
KW - Hypersurface of contact type
KW - Singular potential
KW - Strong force
KW - Variational methods
KW - Weinstein conjecture
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U2 - 10.1016/j.jde.2006.01.021
DO - 10.1016/j.jde.2006.01.021
M3 - Article
AN - SCOPUS:33748278714
VL - 230
SP - 362
EP - 377
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -