Global uniqueness of homoclinic orbits for a class of fourth order equations
type: Item
instance of: scholarly article
title: Global uniqueness of homoclinic orbits for a class of fourth order equations
zbMATH Open document ID: 0766.34027
DOI: 10.1007/BF00946252
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1993-01-16T00:00:00Z
review text: There is a significant class of indefinite Hamiltonian systems for which there are strong and topologically robust theorems on the existence of orbits homoclinic to an equilibrium. In this paper the authors give sufficient conditions for uniqueness of these homoclinic orbits in \(\mathbb{R}^ 4\). Specifically they consider the equivalent equation \(\alpha x''''+\beta x''+\gamma x+k(x)=0\), \(x>0\), where \(\alpha,\gamma>0>\beta\), \(dk/dx<0\) for \(x>0\) and \(k(0)=0\). Uniqueness of homoclinic orbit is established using the maximal principle and some convexity arguments.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 92527
zbMATH Keywords: uniqueness of homoclinic orbit
zbMATH Keywords: indefinite Hamiltonian systems
zbMATH Keywords: existence of orbits
author: Charles J. Amick
author: John F. Toland
reviewed by: B. D. Sleeman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 92527