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Nonlinear Analysis and Semilinear Elliptic Problems


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: January 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521863209

£ 76.99

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About the Authors
  • Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.

    • Contains both classical and more modern advanced techniques and is an ideal introduction to Nonlinear Analysis
    • Ideal for graduate students and academic researchers in Mathematics and Physics
    • Series of Appendices introduces reader to advanced areas of current research
    • Discusses both topological and variational tools
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    Reviews & endorsements

    'In the reviewer's opinion, this book can serve very well as a textbook in topological and variational methods in nonlinear analysis. Even researchers working in this field might find some interesting material (at least the reviewer did).' Zentralblatt MATH

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    Product details

    • Date Published: January 2007
    • format: Hardback
    • isbn: 9780521863209
    • length: 328 pages
    • dimensions: 235 x 158 x 21 mm
    • weight: 0.653kg
    • contains: 55 b/w illus. 28 exercises
    • availability: Available
  • Table of Contents

    1. Preliminaries
    Part I. Topological Methods:
    2. A primer on bifurcation theory
    3. Topological degree, I
    4. Topological degree, II: global properties
    Part II. Variational Methods, I:
    5. Critical points: extrema
    6. Constrained critical points
    7. Deformations and the Palais-Smale condition
    8. Saddle points and min-max methods
    Part III. Variational Methods, II:
    9. Lusternik-Schnirelman theory
    10. Critical points of even functionals on symmetric manifolds
    11. Further results on Elliptic Dirichlet problems
    12. Morse theory
    Part IV. Appendices: Appendix 1. Qualitative results
    Appendix 2. The concentration compactness principle
    Appendix 3. Bifurcation for problems on Rn
    Appendix 4. Vortex rings in an ideal fluid
    Appendix 5. Perturbation methods
    Appendix 6. Some problems arising in differential geometry

  • Authors

    Antonio Ambrosetti, SISSA, Trieste
    Antonio Ambrosetti is a Professor at SISSA, Trieste.

    Andrea Malchiodi, SISSA, Trieste
    Andrea Malchiodi is an Associate Professor at SISSA, Trieste.

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