Critical Point Theory and Its Applications

  • Wenming Zou
  • Martin Schechter

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pages 1-24
  3. Pages 37-54
  4. Pages 117-140
  5. Pages 141-157
  6. Pages 195-213
  7. Pages 215-285
  8. Back Matter
    Pages 287-318

About this book

Introduction

Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications.

The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition.

Audience

This book is intended for advanced graduate students and researchers in mathematics studying the calculus of variations, differential equations and topological methods.

Keywords

Cohomology group Homoclinic orbits Linking Minimum Schrödinger equations Sign-changing solutions calculus compactness extrema

Authors and affiliations

  • Wenming Zou
    • 1
  • Martin Schechter
    • 2
  1. 1.Tsinghua UniversityBeijingChina
  2. 2.University of CaliforniaIrvineUSA

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-32968-4
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-32965-9
  • Online ISBN 978-0-387-32968-0
  • About this book