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  • © 1990

Global Solution Branches of Two Point Boundary Value Problems

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XVIII
  2. Dirichlet branches bifurcating from zero

    • Renate Schaaf
    Pages 1-44
  3. Generalizations

    • Renate Schaaf
    Pages 69-109
  4. General properties of time maps

    • Renate Schaaf
    Pages 110-136
  5. Back Matter

    Pages 137-141

About this book

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

  • Book Title: Global Solution Branches of Two Point Boundary Value Problems

  • Authors: Renate Schaaf

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0098346

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-53514-0Published: 12 December 1990

  • eBook ISBN: 978-3-540-46742-7Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXII, 146

  • Topics: Analysis

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions