An Introduction to Nonlinear Functional Analysis and Elliptic Problems [electronic resource] /
by Antonio Ambrosetti, David Arcoya.
- XII, 199p. 12 illus. online resource.
- Progress in Nonlinear Differential Equations and Their Applications ; 82 .
- 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.
ZDB-2-SMA
This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems.By firstoutlining the advantages and disadvantages of each method, this comprehensive textdisplays how variousapproachescan easily beappliedto a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problemsis divided into two parts: the first discusses keyresults such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, LeraySchauder 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 tosolving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is apractical text for an introductory course or seminar on nonlinear functional analysis.
9780817681142
10.1007/978-0-8176-8114-2 doi
Mathematics. Differentiable dynamical systems. Functional analysis. Differential equations, partial. Mathematics. Functional Analysis. Partial Differential Equations. Dynamical Systems and Ergodic Theory.