Devoted to minimax theorems and their applications to partial differential equations, this text presents these theorems in a simple and unified way, starting from a quantitative deformation lemma. Many applications are given to problems dealing with lack of compactness, especially problems with critical exponents and existence of solitary waves. There are also recent results and some unpublished material, such as a treatment of the generalized Kadomtsev-Petviashvili equation.
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"The material is presented in a unified way, and the proofs are concise and elegant... Essentially self-contained."
--Mathematical Reviews
Willem's book is devoted to minimax theorems and their applications to partial differential equations. Presenting basic minimax theorems in a simple and unified way, this book may serve as a textbook for advanced graduate students in partial differential equations.
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