An Ambrosetti, Antonio. creator author. Arcoya, David. author. SpringerLink (Online service) text xxu 2011 monographic eng

electronic

electronic resource

access XII, 199p. 12 illus. online resource. 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. 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. by Antonio Ambrosetti, David Arcoya. MATHEMATICS DIFFERENTIABLE DYNAMICAL SYSTEMS FUNCTIONAL ANALYSIS DIFFERENTIAL EQUATIONS, PARTIAL MATHEMATICS FUNCTIONAL ANALYSIS PARTIAL DIFFERENTIAL EQUATIONS DYNAMICAL SYSTEMS AND ERGODIC THEORY 515.7 9780817681142 99780817681142 http://dx.doi.org/10.1007/978-0-8176-8114-2 http://dx.doi.org/10.1007/978-0-8176-8114-2 110720 20260521092033.0 978-0-8176-8114-2