The Mountain Pass Theorem

Variants, Generalizations and Some Applications

By: Youssef Jabri

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Paperback | 15 September 2011

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382 Pages

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23.39 x 15.6 x 2.01

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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.

Industry Reviews

Review of the hardback: 'This impressive research monograph provides an excellent basis for an advanced course or a seminar on problems of modern nonlinear analysis.' Zentralblatt MATH

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Calculus of Variations Science Science in General Geometry

Retrospective
First Steps toward the Mountains
Palais-Smale condition. Definitions and examples
Variational principle
Deformation lemma
Reaching the Mountain Pass through Easy Climbs
The finite dimensional MPT
The topological MPT
The classical MPT
The multidimensional MPT
A Deeper Insight in Mountain Topology
The limiting case in the MPT
Palais-Smale condition versus asymptotic behavior
Symmetry and the MPT
The structure of the critical set in the MPT
Weighted Palais-Smale conditions
The Landscape Becoming Less Smooth
The semismooth MPT
The nonsmooth MPT
The metric MPT
Speculating about the Mountain Pass Geometry
The MPT on convex domains
A MPT in order intervals
The linking principle
The intrinsic MPT
Geometrically contrained MPT
Technical Climbs
Numerical MPT implementations
Perturbation from symmetry and the MPT
Applying the MPT in bifurcation problems
More climbs
Background material
Table of Contents provided by Publisher. All Rights Reserved.

The Mountain Pass Theorem

Variants, Generalizations and Some Applications

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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