An introduction to nonlinear functional analysis and elliptic problems
By: Antonio Ambrosetti, David Arcoya
Contributors: Arcoya, David
Series: Progress in nonlinear differential equations and their applications -- v. 82; Progress in nonlinear differential equations and their applications -- v. 82.
Publisher: Birkhaüser
Published: 2011
Place of publication: Boston
Language: eng
Number of pages: 199
ISBN-13: 9780817681135
Subjects: Nonlinear functional analysis; Elliptic Differential equations
Description: 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.
Notes: Includes bibliographical references (p. 193-196) and index.