On the existence of minimal periodic solutions for a class of second-order Hamiltonian systems

被引：2
作者：
Li, Chun [1 ]
Ou, Zeng-Qi [1 ]
Wu, Dong-Lun [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2015年 / 43卷
基金：
中国国家自然科学基金;
关键词：
Minimal periodic solutions; Critical points; Hamiltonian systems; Least action principle; LAGRANGIAN SYSTEMS; OSCILLATIONS; POTENTIALS;
D O I：
10.1016/j.aml.2014.11.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence of minimal periodic solutions for autonomous second-order Hamiltonian systems with even potentials. Some existence results are obtained by using the variational methods. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：44 / 48
页数：5
相关论文
共 30 条
[1]   SOLUTIONS OF MINIMAL PERIOD FOR A CLASS OF CONVEX HAMILTONIAN-SYSTEMS [J].
AMBROSETTI, A ;
MANCINI, G .
MATHEMATISCHE ANNALEN, 1981, 255 (03) :405-421
[2]  
Ambrosetti A., 1987, ANN I H POINCARE-AN, P275
[3]   On the minimal periodic solutions of nonconvex superlinear Hamiltonian systems [J].
An, Tianqing .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :1273-1284
[4]  
[Anonymous], 1989, APPL MATH SCI
[5]   LAGRANGIAN SYSTEMS IN THE PRESENCE OF SINGULARITIES [J].
CAPOZZI, A ;
GRECO, C ;
SALVATORE, A .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 102 (01) :125-130
[6]   PERIODIC-SOLUTIONS OF LAGRANGIAN SYSTEMS WITH BOUNDED POTENTIAL [J].
CAPOZZI, A ;
FORTUNATO, D ;
SALVATORE, A .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 124 (02) :482-494
[7]   HAMILTONIAN TRAJECTORIES HAVING PRESCRIBED MINIMAL PERIOD [J].
CLARKE, FH ;
EKELAND, I .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (02) :103-116
[8]   NON-LINEAR OSCILLATIONS AND BOUNDARY-VALUE-PROBLEMS FOR HAMILTONIAN-SYSTEMS [J].
CLARKE, FH ;
EKELAND, I .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1982, 78 (04) :315-333
[9]  
Degiovanni M., 1988, ANN SCUOLA NORM SUPE, V15, P467
[10]   The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems [J].
Dong, D ;
Long, YM .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (07) :2619-2661
123