Overview
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
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Table of contents (7 chapters)
Keywords
About this book
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 Brezis–Nirenberg 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.
Reviews
From the reviews:
"The book under review presents the contemporary state of the art in critical point theory with strong emphasis on topological methods. … The volume concludes with a rich bibliography of 351 titles, many of them very recent. … advanced, examples included in the text form an excellent review of the frontline of actual research in the area. … In conclusion … very good reference for those seeking new, modern, and powerful techniques in the critical point theory approach of nonlinear differential and partial differential equations." (Vicentiu Radulescu, Mathematical Reviews, Issue 2009 f)
Bibliographic Information
Book Title: Sign-Changing Critical Point Theory
Authors: Wenming Zou
DOI: https://doi.org/10.1007/978-0-387-76657-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2008
Hardcover ISBN: 978-0-387-76657-7Published: 22 September 2008
Softcover ISBN: 978-1-4419-4571-6Published: 05 November 2010
eBook ISBN: 978-0-387-76658-4Published: 15 December 2008
Edition Number: 1
Number of Pages: XIV, 310
Topics: Global Analysis and Analysis on Manifolds, Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Functional Analysis, Topology, Approximations and Expansions