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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.
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Category theory. Homological algebra --- First-order logic. --- Duality theory (Mathematics) --- Toposes. --- First-order logic --- Toposes --- Topoi (Mathematics) --- Categories (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Logic, Modern --- Logic, Symbolic and mathematical --- Duality theory (Mathematics). --- Topos (mathématiques) --- Logique du premier ordre --- Dualité, Principe de (mathématiques) --- Logique du premier ordre.
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Ordered algebraic structures --- Duality theory (Mathematics) --- Groupoids --- Von Neumann algebras --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Group theory --- Algebra --- Mathematical analysis --- Topology --- Dualité, Principe de (mathématiques) --- Von Neumann, Algèbres de --- Groupoïdes --- Von Neumann, Algèbres de. --- Groupoïdes.
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Critical point theory (Mathematical analysis) --- Duality theory (Mathematics) --- Perturbation (Mathematics) --- Point critique, Théorie du (Analyse mathématique) --- Dualité, Principe de (Mathématiques) --- Perturbation (Mathématiques) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- Algebra --- Mathematical analysis --- Topology --- Calculus of variations --- Differential topology --- Global analysis (Mathematics) --- Calculus --- Point critique, Théorie du (Analyse mathématique) --- Dualité, Principe de (Mathématiques) --- Perturbation (Mathématiques)
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