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＜電子ブック＞
An Introduction to Nonlinear Functional Analysis and Elliptic Problems / by Antonio Ambrosetti, David Arcoya Álvarez
(Progress in Nonlinear Differential Equations and Their Applications. ISSN:23740280 ; 82)

版	1st ed. 2011.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2011
大きさ	XII, 199 p. 12 illus : online resource
著者標目	*Ambrosetti, Antonio author Arcoya Álvarez, David author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Differential equations LCSH:Dynamical systems FREE:Functional Analysis FREE:Differential Equations FREE:Dynamical Systems
一般注記	Notation -- Preliminaries -- Some Fixed Point Theorems -- Local and Global Inversion Theorems -- Leray-Schauder Topological Degree -- An Outline of Critical Points -- Bifurcation Theory -- Elliptic Problems and Functional Analysis -- Problems with A Priori Bounds -- Asymptotically Linear Problems -- Asymmetric Nonlinearities -- Superlinear Problems -- Quasilinear Problems -- Stationary States of Evolution Equations -- Appendix A Sobolev Spaces -- Exercises -- Index -- Bibliography This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method, this comprehensive text displays how various approaches can easily be applied to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems is divided into two parts: the first discusses key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray–Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.  The exposition is driven by numerous prototype problems and exposes a variety of approaches to solving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis HTTP:URL=https://doi.org/10.1007/978-0-8176-8114-2

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