Linking Methods in Critical Point Theory

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

    PDF

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 ...

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

"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

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

  Martin Schechter

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