Multiple periodic solutions of Hamiltonian systems with prescribed energy

被引：1

作者：

An, Tianqing ^{[1
]}

机构：

[1] Hohai Univ, Dept Appl Math, Nanjing 210098, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 236卷 / 01期

基金：

中国国家自然科学基金;

关键词：

critical point; Hamiltonian system; hypersurfaces of contact type; periodic solution; positive-type hypersurface;

D O I：

10.1016/j.jde.2007.01.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the periodic solutions of autonomous Hamiltonian systems x = JVH(x) on the given compact energy hypersurface Sigma = H-1 (1). If Sigma is convex or star-shaped, there have been many remarkable contributions for existence and multiplicity of periodic solutions. It is a hard problem to discuss the multiplicity on general hypersurfaces of contact type. In this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star-shaped ones. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：116 / 132

页数：17

共 22 条

[1] The brake orbits of Hamiltonian systems on positive-type hypersurfaces [J].

An, Tianqing .

POSITIVITY, 2006, 10 (04) :681-692

[2] On the number of periodic orbits of Hamiltonian systems on positive-type hypersurfaces in R2n [J].

An, TQ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (04) :633-641

[3] Existence of multiple periodic orbits of Hamiltonian systems on positive-type hypersurfaces in R2n [J].

An, TQ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 278 (02) :376-396

[4] ON CRITICAL-POINT THEORY FOR INDEFINITE FUNCTIONALS IN THE PRESENCE OF SYMMETRIES [J].

BENCI, V .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 274 (02) :533-572

[5] EXISTENCE OF MULTIPLE PERIODIC-ORBITS ON STAR-SHAPED HAMILTONIAN SURFACES [J].

BERESTYCKI, H ;

LASRY, JM ;

MANCINI, G ;

RUF, B .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (03) :253-289

[6] Closed characteristics on partially symmetric compact convex hypersurfaces in R2n [J].

Dong, YJ ;

Long, YM .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 196 (01) :226-248

[7] CONVEX HAMILTONIAN ENERGY SURFACES AND THEIR PERIODIC TRAJECTORIES [J].

EKELAND, I ;

HOFER, H .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1987, 113 (03) :419-469

[8] ON THE NUMBER OF PERIODIC TRAJECTORIES FOR A HAMILTONIAN FLOW ON A CONVEX ENERGY SURFACE [J].

EKELAND, I ;

LASRY, JM .

ANNALS OF MATHEMATICS, 1980, 112 (02) :283-319

[9] PERIODIC-SOLUTIONS OF SUPERQUADRATIC HAMILTONIAN-SYSTEMS [J].

FELMER, PL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 102 (01) :188-207

[10]

GINZBURG V. L., 1995, INT MATH RES NOTICES, P83, DOI [DOI 10.1155/S1073792895000079, 10.1155/S1073792895000079]

← 1 2 3 →