Ebook: Linking Methods in Critical Point Theory
Author: Martin Schechter (auth.)
- Tags: Analysis, Approximations and Expansions, Ordinary Differential Equations, Partial Differential Equations
- Year: 1999
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- 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 ...
Content:
Front Matter....Pages i-xvii
Critical Point Theory....Pages 1-19
Linking....Pages 21-53
Semilinear Boundary Value Problems....Pages 55-72
Alternative Methods....Pages 73-98
Bounded Saddle Point Methods....Pages 99-130
Estimates on Subspaces....Pages 131-144
The Fu??k Spectrum....Pages 145-165
Resonance....Pages 167-204
Boundary Conditions....Pages 205-218
Multiple Solutions....Pages 219-228
Nonlinear Eigenvalues....Pages 229-237
Strong Resonance....Pages 239-253
Notes, Remarks and References....Pages 255-268
Back Matter....Pages 269-294
Content:
Front Matter....Pages i-xvii
Critical Point Theory....Pages 1-19
Linking....Pages 21-53
Semilinear Boundary Value Problems....Pages 55-72
Alternative Methods....Pages 73-98
Bounded Saddle Point Methods....Pages 99-130
Estimates on Subspaces....Pages 131-144
The Fu??k Spectrum....Pages 145-165
Resonance....Pages 167-204
Boundary Conditions....Pages 205-218
Multiple Solutions....Pages 219-228
Nonlinear Eigenvalues....Pages 229-237
Strong Resonance....Pages 239-253
Notes, Remarks and References....Pages 255-268
Back Matter....Pages 269-294
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