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Titlebook: Nonlinear Analysis - Theory and Methods; Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Duš Book 2019 Springer Nature Switzerland AG 2019

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发表于 2025-3-21 18:10:31 | 显示全部楼层 |阅读模式
书目名称Nonlinear Analysis - Theory and Methods
编辑Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Duš
视频video
概述Introduces the basic methods used in the qualitative mathematical analysis of nonlinear models.Reveals a number of surprising interactions between several fields of mathematics, including topology, fu
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Nonlinear Analysis - Theory and Methods;  Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Duš Book 2019 Springer Nature Switzerland AG 2019
描述.This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis..
出版日期Book 2019
关键词35-02, 49-02, 58-02; 35A15, 35A16, 35J25, 35J60, 58E05; Sobolev space; topological degree; variational p
版次1
doihttps://doi.org/10.1007/978-3-030-03430-6
isbn_ebook978-3-030-03430-6Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer Nature Switzerland AG 2019
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Sobolev Spaces,ntegration by parts. In this way we transfer the burden of differentiation from a “bad” (nonsmooth) function, to a “good” (smooth) function. In this chapter, we do not conduct an exhaustive study of Sobolev spaces. This can be found in the specialized books included in the bibliography (see the Remarks at the end of the chapter).
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Compact Operators and Operators of Monotone Type,hap. .). The needs of problems in the calculus of variations and in nonlinear functional equations led to the class of operators of monotone type, which provides a broader framework than the class of compact maps.
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Critical Point Theory,Critical point theory deals with variational problems and so it can be argued that it is as old as calculus. Nevertheless, in its modern form, critical point theory has its roots in the so-called “Dirichlet principle”.
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Morse Theory and Critical Groups,Let . be a Hilbert space with inner product . and let .. By . we denote the Fréchet derivative of . and by . its gradient, that is, . for every . and.
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