Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions
type: Item
instance of: scholarly article
title: Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions
zbMATH Open document ID: 1152.37026
published in: Pacific Journal of Mathematics
publication date: 2008-11-14T00:00:00Z
review text: Let us consider the nonlinear Hamiltonian system \(\frac{dx}{dt}=JH'(t,x(t))\) where \(x(t)\in \mathbb{R}^{2n}\) and \(J\) is the standard symplectic matrix. For a fixed \(L\in \Lambda (n)\)=the set of all Lagrangian subspaces of \(\mathbb{R}^{2n}\) the Lagrangian boundary conditions \(x(0)\in L, x(1)\in L\) are added. Then, the multiplicity of solutions for the above Hamiltonian system with the supplementary hypothesis of asymptotically linearity are studied using a Maslov type theory.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5366262
zbMATH Keywords: index theory
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Lagrangian boundary conditions
author: Chungen Liu
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: pjm.2007.232.233
OpenAlex ID: W2085913943
DOI: 10.2140/PJM.2007.232.233
description: scientific article; zbMATH DE number 5366262