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Global Solution Branches of Two Point Boundary Value Problems

  • Authors
  • Renate┬áSchaaf

Part of the Lecture Notes in Mathematics book series (LNM, volume 1458)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Renate Schaaf
    Pages 1-44
  3. Renate Schaaf
    Pages 69-109
  4. Renate Schaaf
    Pages 110-136
  5. Back Matter
    Pages 137-141

About this book

Introduction

The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations.

Keywords

Bifurkation Boundary value problem Hamiltonian systems Hamiltonsche Gleichungen Randwertprobleme bifurcation boundary value problems differential equation nichtlineare Differentialgleichungen nonlinear differential equations partial differential equation period map

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0098346
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53514-0
  • Online ISBN 978-3-540-46742-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site