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Global Solution Branches of Two Point Boundary Value Problems

  • Book
  • © 1990

Overview

Authors:
  1. Renate Schaaf
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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
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  2. Dirichlet branches bifurcating from zero

    • Renate Schaaf
    Pages 1-44
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  3. Neumann problems, period maps and semilinear dirichlet problems

    • Renate Schaaf
    Pages 45-68
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  4. Generalizations

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

    • Renate Schaaf
    Pages 110-136
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  6. Back Matter

    Pages 137-141
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Keywords

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.

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

  • Industry Sectors: Energy, Utilities & Environment, Engineering, IT & Software

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