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

被引：10

作者：

Carminati, C.

Sere, E.

Tanaka, K.

机构：

[1] Waseda Univ, Sch Sci & Engn, Dept Math, Tokyo, Japan

[2] Univ Pisa, Dept Math, I-56100 Pisa, Italy

[3] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 230卷 / 01期

关键词：

Hamiltonian system; Weinstein conjecture; strong force; singular potential; variational methods; critical point theory; cotangent bundle; closed characteristic; hypersurface of contact type;

D O I：

10.1016/j.jde.2006.01.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a noncompact hypersurface H in R-2N 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. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：362 / 377

页数：16

共 27 条

[1] CRITICAL-POINTS WITH LACK OF COMPACTNESS AND SINGULAR DYNAMICAL-SYSTEMS [J].