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Titlebook: Nonlinear Functional Analysis and its Applications; III: Variational Met Eberhard Zeidler Textbook 1985 Springer Science+Business Media New

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書目名稱Nonlinear Functional Analysis and its Applications
副標(biāo)題III: Variational Met
編輯Eberhard Zeidler
視頻videohttp://file.papertrans.cn/668/667515/667515.mp4
圖書封面Titlebook: Nonlinear Functional Analysis and its Applications; III: Variational Met Eberhard Zeidler Textbook 1985 Springer Science+Business Media New
描述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 gu
出版日期Textbook 1985
關(guān)鍵詞Mathematica; calculus; functional analysis; optimization
版次1
doihttps://doi.org/10.1007/978-1-4612-5020-3
isbn_softcover978-1-4612-9529-7
isbn_ebook978-1-4612-5020-3
copyrightSpringer Science+Business Media New York 1985
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Convexity and Extremal Principles strategy for obtaining existence propositions consists in considering convexity instead of compactness. Figure 39.1 shows the logical connections. We place the Hahn-Banach theorem at the pinnacle; in the final analysis this theorem goes back to the central fixed point theorem of Bourbaki and Kneser
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Lagrange Multipliers and Eigenvalue Problemsconditions. Moreover, we will interpret this condition geometrically and explain the connection with manifolds in B-spaces. In this connection, a generalization of the implicit function theorem is the focal point (Theorem 43.C). The central concepts are:
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Ljusternik-Schnirelman Theory and the Existence of Several Eigenvectorseral eigenvectors for (1) within the generalized context of the Courant maximum-minimum principle. In this connection, in an essential way, we use the fact that . and . are odd potential operators, i.e., . = ., . = ., and .(? .) = ? .(.), .(?.) = ? .(.) for all . ∈ .. We have already explained the b
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otential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert‘s paper showed me that this was not obviously so. Suddenly other certainties about Aristotle‘s (appar
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Eberhard Zeidlerotential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert‘s paper showed me that this was not obviously so. Suddenly other certainties about Aristotle‘s (appar
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