STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

doi:10.1007/s10473-019-0108-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 111-118.doi: 10.1007/s10473-019-0108-7

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

刘春根¹, 张晓飞²

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. School of Mathematics, Nankai University, Tianjin 300071, China

收稿日期:2017-11-01 修回日期:2018-04-08 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Chungen LIU E-mail:liucg@nankai.edu.cn
作者简介:Xiaofei ZHANG,835858094@qq.com
基金资助:
The first author was supported by NSFC (11471170, 11790271), innovation and development project of Guangzhou University.

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

Chungen LIU¹, Xiaofei ZHANG²

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. School of Mathematics, Nankai University, Tianjin 300071, China

Received:2017-11-01 Revised:2018-04-08 Online:2019-02-25 Published:2019-03-13
Contact: Chungen LIU E-mail:liucg@nankai.edu.cn
Supported by:
The first author was supported by NSFC (11471170, 11790271), innovation and development project of Guangzhou University.

摘要/Abstract

摘要： Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions (that is, all its Floquet multipliers lying on the unit circle on the complex plane C).

关键词: Hamiltonian system, the dual Morse index, subharmonic solution, stability

Abstract: Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions (that is, all its Floquet multipliers lying on the unit circle on the complex plane C).

Key words: Hamiltonian system, the dual Morse index, subharmonic solution, stability

刘春根, 张晓飞. STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH[J]. 数学物理学报(英文版), 2019, 39(1): 111-118.

Chungen LIU, Xiaofei ZHANG. STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH[J]. Acta mathematica scientia,Series B, 2019, 39(1): 111-118.

参考文献

[1] Abbondandolo A. Morse Theory for Hamiltonian Systems. London:Chapman, Hall, 2001
[2] An T, Wang Z. Periodic solutions of Hamiltonian systems with anisotropic growth. Commn Pure Appl Anal, 2010, 9:1069-1082
[3] Dell'Antonio G F, D'Onofrio B, Ekeland I. Stability from index estimates for periodic solutions of Lagrangian systems. J Differ Equ, 1994, 108:170-189
[4] D'Onofio B, Ekeland I. Hamiltonian systems with elliptic periodic orbits. Nonlinear Anal, 1990, 14:11-21
[5] Ekeland I. Convexity Methods in Hamiltonian Mechanics. Berlin:Springer, 1990
[6] Fan Z, Zhang D. Stability of the brake orbits on reversible symmetric compact convex hypersurfaces in R²ⁿ. J Fixed Point Theory Appl, 2017, 19:503-527
[7] Fei G. On periodic solutions of superquadratic Hamiltonian systems. Elect J Differ Equ, 2002, 8:1-12
[8] Giradi M, Matzeu M. Dual Morse index estimates for periodic solution of Hamiltonian systems in some nonconvex superquadratic case. Nonlinear Anal, 1991, 17:481-497
[9] Li C, Liu C G. The existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions. Acta Math Sci, 2009, 29B(2):313-326
[10] Liu C. The stability of subharmonic solutions for Hamiltonian systems. J Math Anal Appl, 1999, 240:491-504
[11] Liu C. The stability of the periodic solutions of second order Hamiltonian systems. Chinese Ann Math Ser B, 2000, 21:225-232
[12] Liu C. Dual Morse index for subquadratic Hamiltonian systems and the stability of the closed characteristics (Chinese). Acta Math Sinica (Chin Ser), 2001, 44:1073-1088
[13] Liu C, Long Y. Hyperbolic characteristics on starshaped surfaces. Ann Inst H Poincaré Anal Non linéaire, 1999, 16:725-746
[14] Liu C, Zhang Q. Nontrivial solutions for asymptotically linear Hamiltonian systems with Lagrangian boundary conditions. Acta Math Sci, 2012, 32B(4):1545-1558
[15] Liu C, Zhang X. Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth. Discrete Contin Dyn Syst, 2017, 37:1559-1574
[16] Long Y, Zhu C. Closed characteristics on compact convex hypersurfaces in R²ⁿ. Ann Math, 2002, 155:317-368
[17] Xing Q, Guo F, Zhang X. One generalized critical point theorem and its applications on super-quadratic Hamiltonian systems. Taiwanese J Math, 2016, 20:1093-1116

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

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