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The Mountain Pass Theorem
Variants, Generalizations and Some Applications

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: December 2004
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511056345

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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.

    • 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: December 2004
    • format: Adobe eBook Reader
    • isbn: 9780511056345
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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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