The Mountain Pass Theorem
The Mountain Pass Theorem
Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included.
- More attentive presentation of the theory of min-max methods, exclusively using variants and extensions of ONE THEOREM, the MPT, each of which are treated in a complete and unified way
- Includes a list of MPT versions and extensions and a detailed index
- Comprehensive in both presentation and subject matter
Reviews & endorsements
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
Product details
September 2011Paperback
9781107403338
382 pages
234 × 156 × 20 mm
0.54kg
Available
Table of Contents
- 1. Retrospective
- Part I. First Steps toward the Mountains:
- 2. Palais-Smale condition. Definitions and examples
- 3. Variational principle
- 4. Deformation lemma
- Part II. Reaching the Mountain Pass through Easy Climbs:
- 5. The finite dimensional MPT
- 6. The topological MPT
- 7. The classical MPT
- 8. The multidimensional MPT
- Part III. A Deeper Insight in Mountain Topology:
- 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
- Part IV. The Landscape Becoming Less Smooth:
- 14. The semismooth MPT
- 15. The nonsmooth MPT
- 16. The metric MPT
- Part V. Speculating about the Mountain Pass Geometry:
- 17. The MPT on convex domains
- 18. A MPT in order intervals
- 19. The linking principle
- 20. The intrinsic MPT
- 21. Geometrically contrained MPT
- Part VI. Technical Climbs:
- 22. Numerical MPT implementations
- 23. Perturbation from symmetry and the MPT
- 24. Applying the MPT in bifurcation problems
- 25. More climbs
- Appendix A. Background material.
