Methods in nonlinear integral equations

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Methods in nonlinear integral equations / by Radu Precup

資料種別:: 図書
出版情報:: Dordrecht : Kluwer Academic, c2002
形態:: xiv, 218 p. ; 25 cm
著者名:: Precup, Radu
ISBN:: 9781402008443 [1402008449]
書誌ID:: BA59097925

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注記:

Includes bibliographical references and index

言語:

英語

目次情報:

Preface

Notation

Overview / 0：

Fixed Point Methods / I：

Compactness in Metric Spaces / 1：

Hausdorff's Theorem / 1.1：

The Ascoli-Arzela Theorem / 1.2：

The Frechet-Kolmogorov Theorem / 1.3：

Completely Continuous Operators on Banach Spaces / 2：

Completely Continuous Operators / 2.1：

Brouwer's Fixed Point Theorem / 2.2：

Schauder's Fixed Point Theorem / 2.3：

Continuous Solutions of Integral Equations via Schauder's Theorem / 3：

The Fredholm Integral Operator / 3.1：

The Volterra Integral Operator / 3.2：

An Integral Operator with Delay / 3.3：

The Leray-Schauder Principle and Applications / 4：

The Leray-Schauder Principle / 4.1：

Existence Results for Fredholm Integral Equations / 4.2：

Existence Results for Volterra Integral Equations / 4.3：

The Cauchy Problem for an Integral Equation with Delay / 4.4：

Periodic Solutions of an Integral Equation with Delay / 4.5：

Existence Theory in L[superscript p] Spaces / 5：

The Nemytskii Operator / 5.1：

The Fredholm Linear Integral Operator / 5.2：

The Hammerstein Integral Operator / 5.3：

Hammerstein Integral Equations / 5.4：

Volterra-Hammerstein Integral Equations / 5.5：

References: Part I

Variational Methods / II：

Positive Self-Adjoint Operators in Hilbert Spaces / 6：

Adjoint Operators / 6.1：

The Square Root of a Positive Self-Adjoint Operator / 6.2：

Splitting of Linear Operators in L[superscript p] Spaces / 6.3：

The Frechet Derivative and Critical Points of Extremum / 7：

The Frechet Derivative. Examples / 7.1：

Minima of Lower Semicontinuous Functionals / 7.2：

Application to Hammerstein Integral Equations / 7.3：

The Mountain Pass Theorem and Critical Points of Saddle Type / 8：

The Ambrosetti-Rabinowitz Theorem / 8.1：

Flows and Generalized Pseudo-Gradients / 8.2：

Schechter's Bounded Mountain Pass Theorem / 8.3：

Nontrivial Solutions of Abstract Hammerstein Equations / 9：

Nontrivial Solvability of Abstract Hammerstein Equations / 9.1：

Nontrivial Solutions of Hammerstein Integral Equations / 9.2：

A Localization Result for Nontrivial Solutions / 9.3：

References: Part II

Iterative Methods / III：

The Discrete Continuation Principle / 10：

Perov's Theorem / 10.1：

The Continuation Principle for Contractive Maps on Generalized Metric Spaces / 10.2：

Hammerstein Integral Equations with Matrix Kernels / 10.3：

Monotone Iterative Methods / 11：

Ordered Banach Spaces / 11.1：

Fixed Point Theorems for Monotone Operators / 11.2：

Monotone Iterative Technique for Fredholm Integral Equations / 11.3：

Minimal and Maximal Solutions of a Delay Integral Equation / 11.4：

Methods of Upper and Lower Solutions for Equations of Hammerstein Type / 11.5：

Quadratically Convergent Methods / 12：

Newton's Method / 12.1：

Generalized Quasilinearization for an Integral Equation with Delay / 12.2：

References: Part III

Index

Preface

Notation

Overview / 0：

Fixed Point Methods / I：

Compactness in Metric Spaces / 1：

Hausdorff's Theorem / 1.1：

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