Sign-Changing Critical Point Theory

This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis. It expands on a new theorem that has never before been seen in book form.

Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs.

Key features of this book: (1) Self-contained in-depth treatment of sign-changing critical point theory; (2) Further explorations in Minimax and Morse theories; (3) Topics devoted to linking and nodal solutions, the sign-changing saddle point theory, the generalized BrezisNirenberg critical point theorem, the parameter dependence of sign-changing critical points; (3) Applications of sign-changing critical point theory studied within the classical symmetric mountain pass theorem; (4)Applies sign-changing concepts to Schrödinger equations and boundary value problems.

This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis.

Expands on a new theorem that has never before been seen in book form Explores applications in each chapter that involve Schrödinger equations or Dirichlet boundary value problems Generalizes the Brezis-Nirenberg critical point theorem Solves a vital open question involving the saddle point theory Obtains the relationship between the classical symmetric mountain pass theorem and the sign-changing critical points Proves that Rabinowitz's solutions for perturbed equations are in fact sign-changing Includes supplementary material: sn.pub/extras

Klappentext

Many nonlinear problems in physics, engineering, biology, and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs.

Key features of this book:

• Self-contained in-depth treatment of sign-changing critical point theory

• Further explorations in minimax and Morse theories

• Topics devoted to linking and nodal solutions, the sign-changing saddle point theory, the generalized BrezisNirenberg critical point theorem, the parameter dependence of sign-changing critical points

  * Applications of sign-changing critical point theory studied within the classical symmetric mountain pass theorem

  *Applies sign-changing concepts to Schrödinger equations and boundary value problems

  This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis.

  Also by the author: (with Martin Schechter) Critical Point Theory and Its Applications, ©2006, Springer, ISBN: 978-0-387-32965-9.

  Inhalt
  Preliminaries.- SchechterTintarev Linking.- Sign-Changing Saddle Point.- On a BrezisNirenberg Theorem.- Even Functionals.- Parameter Dependence.- On a BartschChangWangWeth Theory.