The Mountain Pass Theorem: Variants, Generalizations and Some Applications

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Cambridge University Press, 15.09.2003
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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.
 

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Inhalt

Retrospective
7
Definitions and Examples
15
Obtaining Almost Critical Points Variational Principle
22
Obtaining Almost Critical Points The Deformation Lemma
33
The Finite Dimensional MPT
47
The Topological MPT
57
The Classical MPT
65
The Multidimensional MPT
81
The Metric MPT
186
The MPT on Convex Domains
207
MPT in Order Intervals
216
The Linking Principle
226
The Intrinsic MPT
240
Geometrically Constrained MPT
248
Numerical MPT Implementations
259
Perturbation from Symmetry and the MPT
275

The Limiting Case in the MPT
93
PalaisSmale Condition versus Asymptotic Behavior
103
Symmetry and the MPT
114
The Structure of the Critical Set in the MPT
134
Weighted PalaisSmale Conditions
149
The Semismooth MPT
163
TheNonsmoothMPT
174
Applying the MPT in Bifurcation Problems
288
More Climbs
296
A Background Material
315
Bibliography
323
Index
365
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Beliebte Passagen

Seite 325 - A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann.
Seite 327 - Morse theory for symmetric functionals on the sphere and an application to a bifurcation problem, Nonlinear Analysis TMA Vol.
Seite 327 - V. Benci, A geometrical index for the group Sl and some applications to the study of periodic solutions of ordinary differential equations, Comm. Pure Appl. Math. 34 (1981), 393-432.
Seite 327 - On the Morse indices of sign changing solutions of nonlinear elliptic problems. Math. Z., 233, no.

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