Spectral Theory and Nonlinear Functional Analysis

by Julian Lopez-Gomez

Overview

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators. Appealing to a broad audience, it contains many important contributions to linear algebra, linear functional analysis, nonlinear functional analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and systems. The results presented cover a thirty-year period and cut across a variety of mathematical fields.

Product Details

ISBN-13:	9781040202463
Publisher:	CRC Press
Publication date:	03/28/2001
Series:	Chapman & Hall/CRC Research Notes in Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	280
File size:	2 MB

Table of Contents

Introduction. Bifurcation from Simple Eigenvalues. First General Bifurcation Results. The Algebraic Multiplicity. Fundamental Properties of the Multiplicity. Global Bifurcation Theory. Some Applications. Bibliography.

Editorial Reviews

This volume describes pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solution sets presented with minimal use of topological tools. Several applications of the abstract theory to reaction and diffusion equations and systems. The results presented cover a thirty-year period and include recent, previously unpublished findings. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"The book is both an excellent introduction to some novel ideas about nonlinear eigenvalue problems and an exposition of a range of earlier results scattered in different papers and expounded in book form for the first time here."
- Mathematical Reviews, Issue 2002

"This is a nice introductory text about classical functional analysis…" This book will be interesting and useful for many mathematicians, scientists, graduate and undergraduate students."
-Mathematical Reviews

From the Publisher