Multiple homoclinics for a class of singular Hamiltonian systems
type: Item
instance of: scholarly article
title: Multiple homoclinics for a class of singular Hamiltonian systems
zbMATH Open document ID: 0887.58017
author: Paolo Caldiroli
author: C. De Coster
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-08T00:00:00Z
review text: The authors investigate a second order Hamiltonian system of the form \(\ddot u + \nabla V(u) = 0\) in \(\mathbb{R}^n\), where the potential has a unique strict global maximum at the origin \(p\) and a singular set \(S \not\ni p\) such that \(\mathbb{R}^n \backslash S\) is open, path-connected and has non-trivial fundamental group \(\pi_1 = G\). Some additional conditions on behaviour of \(V\) near \(S\) and \(p\) are also assumed so that the class of systems under consideration includes, for instance, the classical \(n\)-body problem. Under some suitable conditions on \(V\) and \(G\) the authors prove the existence of multiple homoclinics, each one belonging to a different class of \(G\).
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 1053439
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: homoclinic solution
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5474
OpenAlex ID: W2057159576
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DOI: 10.1006/JMAA.1997.5474
description: scientific article; zbMATH DE number 1053439