Linking Methods in Critical Point Theory

  • Martin Schechter

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Martin Schechter
    Pages 1-19
  3. Martin Schechter
    Pages 21-53
  4. Martin Schechter
    Pages 55-72
  5. Martin Schechter
    Pages 73-98
  6. Martin Schechter
    Pages 99-130
  7. Martin Schechter
    Pages 131-144
  8. Martin Schechter
    Pages 145-165
  9. Martin Schechter
    Pages 167-204
  10. Martin Schechter
    Pages 205-218
  11. Martin Schechter
    Pages 219-228
  12. Martin Schechter
    Pages 229-237
  13. Martin Schechter
    Pages 239-253
  14. Martin Schechter
    Pages 255-268
  15. Back Matter
    Pages 269-294

About this book

Introduction

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 ...

Keywords

Boundary value problem Eigenvalue Sobolev inequality calculus of variations compactness differential equation equation geometry pdes boundary theorem value problems

Authors and affiliations

  • Martin Schechter
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1596-7
  • Copyright Information Birkhäuser Boston 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7210-6
  • Online ISBN 978-1-4612-1596-7
  • About this book