Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (1): 111-118.doi: 10.1007/s10473-019-0108-7

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

Chungen LIU1, Xiaofei ZHANG2   

  1. 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.

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

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