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Titlebook: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems; Dumitru Motreanu,Viorica Venera Motreanu,Nikol

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發(fā)表于 2025-3-21 16:33:58 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems
編輯Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos
視頻videohttp://file.papertrans.cn/927/926445/926445.mp4
概述Parallel treatment of smooth and nonsmooth problems.Contains proofs for many of the results stated herein.Presents recent research in the field for the first time in book form
圖書封面Titlebook: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems;  Dumitru Motreanu,Viorica Venera Motreanu,Nikol
描述This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in th
出版日期Book 2014
關(guān)鍵詞Convex function; Degree theory; Minimization; Morse theory; Nonlinear operators; Sobolev spaces; partial d
版次1
doihttps://doi.org/10.1007/978-1-4614-9323-5
isbn_softcover978-1-4939-4474-3
isbn_ebook978-1-4614-9323-5
copyrightSpringer Science+Business Media, LLC 2014
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Nonsmooth Analysis,eing a maximal monotone operator. The second section has as its main focus the subdifferentiability theory for locally Lipschitz functions. Further information and references are indicated in a remarks section.
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Nonlinear Operators,solutions to nonlinear equations. Specifically, they are useful in the study of nonlinear elliptic boundary value problems as demonstrated in the final three chapters of the present book. The first section of the chapter is devoted to compact operators and emphasizes the spectral properties, includi
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Variational Principles and Critical Point Theory,he case of nonlinear elliptic boundary value problems. The first section of the chapter illustrates the connection between the variational principles of Ekeland and Zhong and compactness-type conditions such as the Palais–Smale and Cerami conditions. The second section contains the deformation theor
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Morse Theory, solutions of nonlinear elliptic boundary value problems with a variational structure. The first section of the chapter contains the needed preliminaries of algebraic topology. The second section focuses on the Morse lemma and the splitting and shifting theorems. The third section is devoted to the
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Regularity Theorems and Maximum Principles,ear elliptic boundary value problems. In addition to the presentation of fundamental results, the chapter offers, to a large extent, a novel approach with clarification of tedious arguments and simplification of proofs. The first section of this chapter treats two major topics related to weak soluti
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