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Titlebook: Methods of Nonlinear Analysis; Applications to Diff Pavel Drábek,Jaroslav Milota Textbook 2013Latest edition Springer Basel 2013 boundary v

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书目名称Methods of Nonlinear Analysis
副标题Applications to Diff
编辑Pavel Drábek,Jaroslav Milota
视频video
概述Designed as a textbook for advanced undergraduate and graduate students and useful as a handbook for scientists and engineers.Two level structure: basic level for the beginners and advanced one for mo
丛书名称Birkhäuser Advanced Texts‘ Basler Lehrbücher
图书封面Titlebook: Methods of Nonlinear Analysis; Applications to Diff Pavel Drábek,Jaroslav Milota Textbook 2013Latest edition Springer Basel 2013 boundary v
描述.In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently. .In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question..The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists.
出版日期Textbook 2013Latest edition
关键词boundary value problem; evolution equation; functional analysis; nonlinear analysis; ordinary and partia
版次2
doihttps://doi.org/10.1007/978-3-0348-0387-8
isbn_softcover978-3-0348-0759-3
isbn_ebook978-3-0348-0387-8Series ISSN 1019-6242 Series E-ISSN 2296-4894
issn_series 1019-6242
copyrightSpringer Basel 2013
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Properties of Linear and Nonlinear Operators,In this section we point out some fundamental properties of linear operators in Banach spaces. The key assertions presented are the Uniform Boundedness Principle, the Banach–Steinhaus Theorem, the Open Mapping Theorem, the Hahn–Banach Theorem, the Separation Theorem, the Eberlain–Smulyan Theorem and the Banach Theorem.
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Monotonicity Methods,The motivation for the methods presented in this section can be described by the following simple example of a real function of one real variable . We would like to find conditions on . which guarantee that for any . the equation .(.) = . has a (unique) solution ..
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Some Applications to Partial Differential Equations,We remind the reader that .. was constructed in Exercise 3.1.28(ii) provided . was a densely defined self-adjoint operator with a compact resolvent and with the spectrum bounded from above. In this section we generalize .. for a rather general class of linear operators . : . on a Banach space ..
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