An Invitation to Variational Methods in Differential Equations

  • David G. Costa

Table of contents

  1. Front Matter
    Pages i-xii
  2. David G. Costa
    Pages 1-5
  3. David G. Costa
    Pages 7-18
  4. David G. Costa
    Pages 19-27
  5. David G. Costa
    Pages 29-38
  6. David G. Costa
    Pages 39-47
  7. David G. Costa
    Pages 49-62
  8. David G. Costa
    Pages 63-73
  9. David G. Costa
    Pages 75-85
  10. David G. Costa
    Pages 87-97
  11. David G. Costa
    Pages 99-113
  12. David G. Costa
    Pages 115-124
  13. David G. Costa
    Pages 125-129
  14. Back Matter
    Pages 131-138

About this book

Introduction

This book is a short introductory text to variational techniques with applications to differential equations. It presents a sampling of topics in critical point theory with applications to existence and multiplicity of solutions in nonlinear problems involving ordinary differential equations (ODEs) and partial differential equations (PDEs).

Five simple problems in ODEs which illustrate existence of solutions from a variational point of view are introduced in the first chapter. These problems set the stage for the topics covered, including minimization, deformation results, the mountain-pass theorem, the saddle-point theorem, critical points under constraints, a duality principle, critical points in the presence of symmetry, and problems with lack of compactness. Each topic is presented in a straightforward manner, and followed by one or two illustrative applications.

The concise, straightforward, user-friendly approach of this textbook will appeal to graduate students and researchers interested in differential equations, analysis, and functional analysis.

Keywords

Boundary value problem critical points nonlinear analysis ordinary differential equation partial differential equation

Authors and affiliations

  • David G. Costa
    • 1
  1. 1.Department of Mathematical SciencesUniversity of Nevada, Las VegasLas VegasUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4536-6
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4535-9
  • Online ISBN 978-0-8176-4536-6
  • About this book