Building on min-max methods, Professor Ghoussoub systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole new 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 self-contained.
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The calculus of variations is a method for finding stable solutions to optimization problems. To find unstable ones, Morse theory and min-max methods are more appropriate, despite difficulties in applying them universally. Professor Ghoussoub describes a new point of view that may help when dealing with such difficulties. Building upon min-max approach, he systematically develops a general theory and presents a whole new array of duality and perturbation methods. The the book reasonably self-contained. Consequently, it should be accessible to all mathematicians,economists and engineers working in nonlinear analysis or optimization.
"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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