An Introduction to Nonlinear Functional Analysis and Elliptic Problems

• Main Authors: Ambrosetti, Antonio (Author), Arcoya, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2011.
• Series: Progress in Nonlinear Differential Equations and Their Applications ; 82
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Partial differential equations.; Functional Analysis.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.

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 ...

Table of Contents:

• 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.