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

Abstract

<abstract><p>In this paper, we give the relation between a relative Morse index for two continuous symmetric matrices paths in $ {{\bf R}}^{2n} $ 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.</p></abstract>