Maslov type index theory for linear Hamiltonian systems with Bolza boundary value conditions and multiple solutions for nonlinear Hamiltonian systems

Yujun Dong

Vol. 221 (2005), No. 2, 253–280

DOI: 10.2140/pjm.2005.221.253

Abstract

We study the classification of linear Hamiltonian systems satisfying Bolza boundary conditions and its applications to nonlinear Hamiltonian systems.

Keywords

Hamiltonian system, Bolza problem, existence and multiplicity of solutions, Maslov type index theory, relative Morse index, μ-index, Leray–Schauder degree theory, dual variational principle, Morse theory

Mathematical Subject Classification 2000

Primary: 34B15

Milestones

Received: 26 January 2004

Revised: 27 August 2004

Accepted: 27 August 2004

Published: 1 October 2005