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Nonlinear Functional Analysis and its Applications
E. Zeidler
其他書名
III: Variational Methods and Optimization
出版Springer Science & Business Media, 2013-12-11
主題Science / System TheoryMathematics / CalculusMathematics / Mathematical AnalysisLanguage Arts & Disciplines / Library & Information Science / GeneralMathematics / GeneralMathematics / Functional Analysis
ISBN146125020X9781461250203
URLhttp://books.google.com.hk/books?id=xALaBwAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.