An Introduction to Nonlinear Functional Analysis and Elliptic Problems

  • Antonio Ambrosetti
  • David Arcoya

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 82)

Table of contents

  1. Front Matter
    Pages 1-1
  2. Antonio Ambrosetti, David Arcoya
    Pages 1-15
  3. Antonio Ambrosetti, David Arcoya
    Pages 17-21
  4. Antonio Ambrosetti, David Arcoya
    Pages 23-31
  5. Antonio Ambrosetti, David Arcoya
    Pages 33-45
  6. Antonio Ambrosetti, David Arcoya
    Pages 47-60
  7. Antonio Ambrosetti, David Arcoya
    Pages 61-72
  8. Antonio Ambrosetti, David Arcoya
    Pages 73-82
  9. Antonio Ambrosetti, David Arcoya
    Pages 83-96
  10. Antonio Ambrosetti, David Arcoya
    Pages 97-110
  11. Antonio Ambrosetti, David Arcoya
    Pages 111-119
  12. Antonio Ambrosetti, David Arcoya
    Pages 121-129
  13. Antonio Ambrosetti, David Arcoya
    Pages 131-147
  14. Antonio Ambrosetti, David Arcoya
    Pages 149-168
  15. Back Matter
    Pages 163-163

About this book

Introduction

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.

Keywords

Leray--Schauder topological degree bifurcation theory critical points elliptic problems fixed point theorem global inversion theorems nonlinear functional analysis quasilinear problems suprelinear problems

Authors and affiliations

  • Antonio Ambrosetti
    • 1
  • David Arcoya
    • 2
  1. 1.Department of MathematicsSISSATriesteItaly
  2. 2.Facultad de Ciencias, Departamento de Análisis MatemáticoUniversidad GranadaGranadaSpain

Bibliographic information