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1993 (4)

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Duality and perturbation methods in critical point theory
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ISBN: 0511551703 Year: 1993 Publisher: Cambridge : Cambridge University Press,

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Abstract

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.

Duality and definability in first order logic
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ISBN: 0821825658 9780821825655 Year: 1993 Volume: 503 Publisher: Providence, R.I. American Mathematical Society

Duality for actions and coactions of measured groupoids on von Neumann algebras
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ISBN: 0821825453 Year: 1993 Publisher: Providence, R.I. American Mathematical Society

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