Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems
type: Item
instance of: scholarly article
title: Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems
zbMATH Open document ID: 1193.37080
author: Boris Buffoni
author: Laurent Landry
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-05-06T00:00:00Z
review text: Let \(m\geq 2\) and the potential \(V:\mathbb{R}^m\rightarrow \mathbb{R}, V(q)=-|q|^2/2+W(q, \dot{q})\). A set of five hypothesis about \(W\) are considered in order to prove the existence of at least two non-trivial homoclinic orbits for the Lagrangian system associated to \(V\). The autonomous case \(W=W(q)\) covers the results of \textit{A. Ambrosetti} and \textit{V. Coti Zelati} [Rend. Semin. Mat. Univ. Padova 89, 177--194 (1993; Zbl 0806.58018)] where \(W\in C^2(\mathbb{R}^m, \mathbb{R})\) is superquadratic, satisfies a ``pinching'' hypothesis and also an hypothesis on its second derivative.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 5704393
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: Lagrangian systems
zbMATH Keywords: variational methods
zbMATH Keywords: critical-point theory
zbMATH Keywords: minimax method
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: dcds.2010.27.75
OpenAlex ID: W2160566474
DOI: 10.3934/DCDS.2010.27.75
Recommended article: Homoclinic orbits for Lagrangian systems
Recommended article: Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
Recommended article: Multiple homoclinic orbits for a class of conservative systems
Recommended article: Multiple homoclinic orbits for autonomous, singular potentials
Recommended article: Q4849521
Recommended article: Homoclinic solutions of quasiperiodic Lagrangian systems
Recommended article: Multiple homoclinic orbits for a class of Hamiltonian systems.
Recommended article: Q4449424
Recommended article: Homoclinic orbits in generalized Liénard systems
Recommended article: Homoclinic orbits of positive definite Lagrangian systems
description: scientific article; zbMATH DE number 5704393