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Field name	Details
Dewey Class	515.7
Title	An Introduction to Nonlinear Functional Analysis and Elliptic Problems ([Ebook]) / by Antonio Ambrosetti, David Arcoya.
Author	Ambrosetti, Antonio
Added Personal Name	Arcoya, David
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser, , 2011.
Physical Details	XII, 199 pages: 12 illus. : online resource.
Series	Progress in nonlinear differential equations and their applications ; 82
ISBN	9780817681142
Summary Note	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.Â 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 aÂ practical text for an introductory course or seminar on nonlinear functional analysis.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8114-2
Links to Related Works	Subject References: Differentiable dynamical systems . Differential equations, Partial . Dynamical systems and ergodic theory . Functional Analysis . Mathematics . Partial differential equations . Authors: Ambrosetti, Antonio . Arcoya, David . author . Corporate Authors: SpringerLink (Online service) . Series: Progress in nonlinear differential equations and their applications . Classification: 515.7 . 515.7 (DDC 23) .

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An Introduction to Nonlinear Functional Analysis and Elliptic Problems

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