00000cmm a22000004a 4500 UP-99796217611212089 Buklod 20250128110147.0 m go j cr |nu|||auu|a 250128s2011 xxu o j | eng d 9780817681142 (eBook) 0817681140 (eBook) (iLib)UPD-00214608248 DLC DMLR rda eng DMLUC QA 377 A5664 2011eb Ambrosetti, A. (Antonio) author. An introduction to nonlinear functional analysis and elliptic problems [electronic resource] Antonio Ambrosetti, David Arcoya. Boston, Massachusetts Birkhäuser Boston, MA 2011. 1 online resource (xii, 209 pages) illustrations. text rdacontent computer rdamedia online resource rdacarrier Progress in Nonlinear Differential Equations and Their Applications 82 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Differential equations, Elliptic. Nonlinear functional analysis. Differential equations, Partial. SpringerLink (Online service). Electronic resource Available for UP System via Springer Link. https://doi.org/10.1007/978-0-8176-8114-2 FO UPD DMLR QA 377 A5664 2011eb Electronic Resource