The existence of homoclinic orbits for Hamiltonian systems with the potentials changing sign
type: Item
instance of: scholarly article
title: The existence of homoclinic orbits for Hamiltonian systems with the potentials changing sign
zbMATH Open document ID: 0871.58036
author: Guihua Fei
published in: Chinese Annals of Mathematics. Series B
publication date: 1997-09-08T00:00:00Z
review text: The paper deals with second order Hamiltonian systems of the form \[ q''-L(t)q+b(t)\text{grad}W(q)=0, \] where \(q\in\mathbb{R}^n\), \(L(t)\) is a symmetric positive definite matrix, and the function \(b(t)\) can change sign. The aim is to find non-trivial homoclinic orbits through 0. The author proves three theorems giving the conditions for existence of these orbits. The existence of homoclinic orbits of such systems has been studied by many mathematicians, and the considered generalization concerns a new kind of ``superquadratic'' condition on \(W\) and the assumption changing sign of function \(b(t)\); in so doing \(b(t)\) may be non-periodic.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 978283
zbMATH Keywords: Hamiltonians systems
zbMATH Keywords: homoclinic orbits
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 978283