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Spectral Theory and Nonlinear Functional Analysis

Spectral Theory and Nonlinear Functional Analysis by Julian Lopez-Gomez
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INTRODUCTION
General Assumptions and Basic Concepts
Some New Results
Historical Remarks
BIFURCATION FROM SIMPLE EIGENVALUES
Simple Eigenvalues and Transversality
The Theorem of M.G. Crandall and P.H. Rabinowitz
Local Bifurcation Diagrams
The Exchange Stability Principle
Applications
FIRST GENERAL BIFURCATION RESULTS
Lyapunov-Schmidt Reductions
The theorem of J. Ize
The Global Alternative of P.H. Rabinowitz
The Theorem of D. Westreich
THE ALGEBRAIC MULTIPLICITY
Motivating the Concept of Transversality
Transversal Eigenvalues
Algebraic Eigenvalues
Analytic Families
Simple Degenerate Eigenvalues
FUNDAMENTAL PROPERTIES OF THE MULTIPLICITY
The Multiplicity of R.J. Magnus
Relations between c and m
The Fundamental Theorem
The Classical Algebraic Multiplicity
Finite Dimensional Characterizations
The Parity of the Crossing Number
GLOBAL BIFURCATION THEORY
Preliminaries
Local Bifurcation
Global Behavior of the Bounded Components
Unilateral Global Bifurcation
Unilateral Bifurcation for Positive Operators
APPLICATIONS
Positive Solutions o Semilinear Elliptic Problems
Coexistence States for Elliptic Systems
Examples
A Further Application
REFERENCES
INDEX
CRC Press; March 2001
281 pages; ISBN 9781420035506
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Title: Spectral Theory and Nonlinear Functional Analysis
Author: Julian Lopez-Gomez
 
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