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Research Article | Open Access

Multiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems

Jiachen Mu, Duanzhi Zhang( )
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
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Abstract

In this paper, we give the relation between a relative Morse index for two continuous symmetric matrices paths in R 2 n satisfying condition (BS1) and the Maslov-type indices under symmetric brake orbit boundary value of these two symmetric matrices paths. As application, we obtain a multiple existence of symmetric brake orbit solutions of asymptotically linear symmetric reversible Hamiltonian systems.

Keywords

symmetric brake orbitsreversibleHamiltonian systemsMaslov-type indexasymptotic linear

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Electronic Research Archive
Volume 30 Issue 7,
July 2022
Pages 2417-2427
DOI: 10.3934/era.2022123

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Cite this article:
Mu J, Zhang D. Multiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems. Electronic Research Archive, 2022, 30(7): 2417-2427. https://doi.org/10.3934/era.2022123

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Received: 29 September 2021
Revised: 20 December 2021
Accepted: 25 December 2021
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)