Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
type: Item
instance of: scholarly article
title: Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
zbMATH Open document ID: 0802.34052
author: Piero Montecchiari
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1994-07-13T00:00:00Z
full work available at URL: https://eudml.org/doc/244177
review text: Let us consider the asymptotically periodic Hamiltonian system (1) \(\ddot q= q-\text{grad }V(t,q)\), \(q\in \mathbb{R}^ m\), that means, \(U(t,q)\) exists such that \(U(t+ T,q)= U(t,q)\) for all \((t,q)\in \mathbb{R}\times \mathbb{R}^ m\) and \(|\text{grad }V(t,q)- \text{grad }U(t,q)|\to 0\) as \(t\to- \infty\), uniformly on the compacts of \(\mathbb{R}^ m\). Under certain conditions, the author proved the existence of infinitely many homoclinic solutions of (1). The obtained solutions are so-called \(k\)-bump solutions \(k\in N\), that means the \(k\)-bump solutions go away from zero and return near it, \(k\) times.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 591105
zbMATH Keywords: asymptotically periodic Hamiltonian system
zbMATH Keywords: infinitely many homoclinic solutions
zbMATH Keywords: \(k\)-bump solutions
reviewed by: A. Klíč
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 591105