Spectral theory and nonlinear functional analysis

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Spectral theory and nonlinear functional analysis / Julián López-Gómez

資料種別:: 図書
出版情報:: Boca Raton, Fla. : Chapman & Hall/CRC, c2001
形態:: xii, 265 p. ; 24 cm
シリーズ名:: Research notes in mathematics ; 426 <BA41222266>
著者名:: López-Gómez, Julián
ISBN:: 9781584882497 [1584882492]
書誌ID:: BA51657210

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注記:

Bibliography: p. 251-260
Includes index

主題:

Nonlinear functional analysis; Spectral theory (Mathematics)

言語:

英語

目次情報:

Preface

Introduction / 1.：

General assumptions and basic concepts / 1.1：

Some new results / 1.2：

Historical remarks / 1.3：

Bifurcation from simple eigenvalues / 2.：

Simple eigenvalues and transversality / 2.1：

The theorem of M. G. Crandall and P. H. Rabinowitz / 2.2：

Local bifurcation diagrams / 2.3：

The exchange stability principle / 2.4：

Applications / 2.5：

A simple application / 2.5.1：

The Selkov scheme for glycolysis / 2.5.2：

First general bifurcation results / 3.：

Lyapunov-Schmidt reductions / 3.1：

The theorem of J. Ize / 3.2：

The global alternative of P. H. Rabinowitz / 3.3：

The theorem of D. Westreich / 3.4：

The algebraic multiplicity / 4.：

Motivating the concept of transversality / 4.1：

Transversal eigenvalues / 4.2：

Algebraic eigenvalues / 4.3：

Analytic families / 4.4：

Simple degenerate eigenvalues / 4.5：

Other fundamental properties of the multiplicity / 5.：

The multiplicity of R. J. Magnus / 5.1：

Relations between x and [mu] / 5.2：

The fundamental theorem / 5.3：

The classical algebraic multiplicity / 5.4：

Finite dimensional characterizations / 5.5：

The parity of the crossing number / 5.6：

Global bifurcation theory / 6.：

Preliminaries / 6.1：

Local bifurcation / 6.2：

Global behavior of the bounded components / 6.3：

Unilateral global bifurcation / 6.4：

Unilateral bifurcation for positive operators / 6.5：

Positive solutions of semilinear elliptic problems / 7.：

Coexistence states for elliptic systems / 7.2：

Examples / 7.3：

Example 1 / 7.3.1：

Example 2 / 7.3.2：

Example 3 / 7.3.3：

A further application / 7.4：

References

Index

Preface

Introduction / 1.：

General assumptions and basic concepts / 1.1：

Some new results / 1.2：

Historical remarks / 1.3：

Bifurcation from simple eigenvalues / 2.：

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