The mountain pass theorem : variants, generalizations and some applications / Youssef Jabri.
Material type:
TextSeries: Encyclopedia of mathematics and its applications ; v. 95.Publication details: Cambridge ; New York : Cambridge University Press, 2003.Description: 1 online resource (xii, 369 pages) : illustrationsContent type: - text
- computer
- online resource
- 0511062672
- 9780511062674
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- Mountain pass theorem
- Critical point theory (Mathematical analysis)
- Hamiltonian systems
- Variational principles
- Variational inequalities (Mathematics)
- Maxima and minima
- Nonsmooth optimization
- Théorème du col
- Théorie des points critiques (Analyse mathématique)
- Systèmes hamiltoniens
- Principes variationnels
- Inégalités variationnelles
- Maximums et minimums
- Optimisation non différentiable
- MATHEMATICS -- Calculus
- MATHEMATICS -- Mathematical Analysis
- Hamiltonian systems
- Variational principles
- Variational inequalities (Mathematics)
- Maxima and minima
- Nonsmooth optimization
- Mountain pass theorem
- Critical point theory (Mathematical analysis)
- Critical point theory (Mathematical analysis)
- Hamiltonian systems
- Maxima and minima
- Mountain pass theorem
- Nonsmooth optimization
- Variational inequalities (Mathematics)
- Variational principles
- Kritischer Punkt Mathematik
- Plateau-Problem
- 515/.64 22
- QA614.7 .J33 2003eb
- O176. 3
- O17
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Includes bibliographical references (pages 323-364) and index.
Print version record.
Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Introduction; 1 Retrospective; 2 Palais-Smale Condition: Definitions and Examples; 3 Obtaining "Almost Critical Points" -- Variational Principle; 4 Obtaining "Almost Critical Points" -- The Deformation Lemma; 5 The Finite Dimensional MPT; 6 The Topological MPT; 7 The Classical MPT; 8 The Multidimensional MPT; 9 The Limiting Case in the MPT; 10 Palais-Smale Condition versus Asymptotic Behavior; 11 Symmetry and the MPT; 12 The Structure of the Critical Set in the MPT; 13 Weighted Palais-Smale Conditions.
This book presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The coverage includes standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. 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.
English.
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