© 2020

Critical Point Theory

Sandwich and Linking Systems


  • Collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points

  • Presents numerous applications of critical point theory to important problems in mathematics and physics

  • Includes many of the author’s own state-of-the-art contributions to this active area of research


Table of contents

  1. Front Matter
    Pages i-xxxvi
  2. Martin Schechter
    Pages 1-20
  3. Martin Schechter
    Pages 21-29
  4. Martin Schechter
    Pages 31-46
  5. Martin Schechter
    Pages 47-60
  6. Martin Schechter
    Pages 61-81
  7. Martin Schechter
    Pages 83-93
  8. Martin Schechter
    Pages 95-111
  9. Martin Schechter
    Pages 113-130
  10. Martin Schechter
    Pages 131-165
  11. Martin Schechter
    Pages 167-190
  12. Martin Schechter
    Pages 191-211
  13. Martin Schechter
    Pages 213-224
  14. Martin Schechter
    Pages 225-242
  15. Martin Schechter
    Pages 243-253
  16. Martin Schechter
    Pages 255-260
  17. Martin Schechter
    Pages 261-276
  18. Martin Schechter
    Pages 277-291
  19. Martin Schechter
    Pages 293-306
  20. Back Matter
    Pages 307-320

About this book


This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied.

Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book’s main subject: applications to problems in mathematics and physics. These include topics such as Schrödinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout.

Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.


Critical point theory Critical point calculus Critical point theory applications Variational methods Variational methods mathematical physics Saddle point theory Sandwich sets Infinite dimensional linking Weak solutions Minimax systems Semilinear differential equations Semilinear differential systems Semilinear partial differential equations Sandwich systems Sandwich pairs Monotonicity Schrodinger equation Elliptic systems Semilinear wave equation Hamiltonian systems

Authors and affiliations

  1. 1.BrooklynUSA

Bibliographic information

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“Many problems arizing in science and engineering call for the solving of nonlinear ordinary differential equations or partial differential equations. These equations are difficult to solve, and there are few general techniques … to solve them. … This has motivated researchers to study critical points of functionals in order to solve the corresponding Euler equations. It has led to the development of several techniques to find critical points. This book is dedicated to the latest developments and applications of these techniques.” (Mohsen Timoumi, zbMATH 1462.35008, 2021)