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  3. Duality and Perturbation Methods in Critical Point Theory
  • Cited by 223
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1993
Online ISBN:
9780511551703
DOI:
https://doi.org/10.1017/CBO9780511551703
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (107)
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Book description

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

Reviews

"The excellent material presentation of this small book follows the tradition of the series." Jean Mawhin, SIAM Review

"...I recommend Ghoussoub's book to anyone working on variational problems, in particular on LS-theory. The reader will find a systematic presentation and detailed exposition of useful techniques." T. Bartsch, Bulletin of the American Mathematical Society

"...Each chapter ends with some historical notes and comments, which offer a very useful guide through the literature on the subjects mentioned." Maria Letizia Bertotti, Mathematical Reviews

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