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Birkhäuser

Linking Methods in Critical Point Theory

  • Book
  • © 1999

Overview

Authors:
  1. Martin Schechter

    1. Department of Mathematics, University of California, Irvine, USA

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Critical Point Theory

    • Martin Schechter
    Pages 1-19

  3. Linking

    • Martin Schechter
    Pages 21-53

  4. Semilinear Boundary Value Problems

    • Martin Schechter
    Pages 55-72

  5. Alternative Methods

    • Martin Schechter
    Pages 73-98

  6. Bounded Saddle Point Methods

    • Martin Schechter
    Pages 99-130

  7. Estimates on Subspaces

    • Martin Schechter
    Pages 131-144

  8. The Fučík Spectrum

    • Martin Schechter
    Pages 145-165

  9. Resonance

    • Martin Schechter
    Pages 167-204

  10. Boundary Conditions

    • Martin Schechter
    Pages 205-218

  11. Multiple Solutions

    • Martin Schechter
    Pages 219-228

  12. Nonlinear Eigenvalues

    • Martin Schechter
    Pages 229-237

  13. Strong Resonance

    • Martin Schechter
    Pages 239-253

  14. Notes, Remarks and References

    • Martin Schechter
    Pages 255-268

  15. Back Matter

    Pages 269-294
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Keywords

About this book

As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif­ ferential equations? To find out, read on ...

Reviews

"The main merit of this work is the utmost clearness through which the author explains some subjects connected with very strong technical difficulties... The particular way used...to introduce the basic aspects of linking methods will be very encouraging and stimulating for young researchers... The book may be warmly recommended to all specialists in this fascinating field of current interest and growing importance."

--ZAA

"The book is addressed to mathematicians and students interested in critical points in any context...recommended also for researchers in the fields of pdes and nonlinear analysis... This reviewer calls the attention of the designers of algorithms for determining critical points to this book as a possible theoretical basis for new powerful numerical methods."

--Acta Sci. Math

Authors and Affiliations

  • Department of Mathematics, University of California, Irvine, USA

    Martin Schechter

Bibliographic Information

  • Book Title: Linking Methods in Critical Point Theory

  • Authors: Martin Schechter

  • DOI: https://doi.org/10.1007/978-1-4612-1596-7

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-8176-4095-8Published: 01 July 1999

  • Softcover ISBN: 978-1-4612-7210-6Published: 06 October 2012

  • eBook ISBN: 978-1-4612-1596-7Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVII, 294

  • Topics: Analysis, Approximations and Expansions, Ordinary Differential Equations, Partial Differential Equations

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