Volume no :9, Issue no: 1, September (2018)

International Journal of Applied Mathematics and Machine Learning

SUBHARMONIC SOLUTIONS OF SUBQUADRATIC HAMILTONIAN SYSTEMS AND THE MASLOV-TYPE INDEX THEORY

Author's: Chong Li
Pages: [11] - [26]
Received Date: August 10, 2018
Submitted by: Li Li.
DOI: http://dx.doi.org/10.18642/ijamml_7100121998

Abstract

In this paper, we mainly use the Galerkin approximation method and the iteration inequalities of the Maslov type index theory to study the properties of subharmonic solutions for the Hamiltonian systems where is a semipositive symmetric continuous matrix and is unbounded. We prove that these Hamiltonian systems exist subharmonic solutions, and these solutions are pairwise geometrically distinct under certain conditions.

Keywords

subharmonic solution, Maslov-type index, Hamiltonian systems.