A Study of heteroclinic orbits for a class of fourth order ordinary differential equations

Première édition

In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.

Livre broché - En anglais 17,90 €

InfoPour plus d'informations à propos de la TVA et d'autres moyens de paiement, consultez la rubrique "Paiement & TVA".


Presses universitaires de Louvain
Partie du titre
Numéro 1
Denis Bonheure,
Thèses de la Faculté des sciences
Catégorie (éditeur)
Sciences exactes > Mathématiques > Analyse mathématique
Catégorie (éditeur)
Sciences exactes > Mathématiques
Catégorie (éditeur)
Sciences exactes
BISAC Subject Heading
Code publique Onix
06 Professionnel et académique
CLIL (Version 2013-2019 )
Date de première publication du titre
01 janvier 2004
Type d'ouvrage

Livre broché

Date de publication
01 janvier 2004
Nombre de pages de contenu principal : 217
Code interne
16 x 24 x 1,2 cm
353 grammes
17,90 €
Version 2.1, Version 3

Google Livres Aperçu

Publier un commentaire sur cet ouvrage


Préface vii

Avant-propos xi

Liste des publications lix

A Study of Heteroclinic Orbits for a Class of Fourth Order Ordinary Differential Equations 1

Contents 3

Introduction 5

An overview 7