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The Mountain Pass Theorem
Variants, Generalizations and Some Applications

$87.95 (R)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: September 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107403338

$ 87.95 (R)

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About the Authors
  • 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
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    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

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    Product details

    • Date Published: September 2011
    • format: Paperback
    • isbn: 9781107403338
    • length: 382 pages
    • dimensions: 234 x 156 x 20 mm
    • weight: 0.54kg
    • availability: 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.

  • Author

    Youssef Jabri, Mohammed First University, Oujda

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