Ebook: Existence Theory for Nonlinear Integral and Integrodifferential Equations
- Tags: Integral Equations, Operator Theory, Ordinary Differential Equations, Functional Analysis
- Series: Mathematics and Its Applications 445
- Year: 1998
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.
Content:
Front Matter....Pages i-ix
Introduction and Preliminaries....Pages 1-13
Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations....Pages 14-36
Solution Sets of Abstract Volterra Equations....Pages 37-45
Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Compact Intervals....Pages 46-64
Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Half-Open Intervals....Pages 65-108
Existence Theory for Nonlinear Nonresonant Operator and Integral Equations....Pages 109-127
Existence Theory for Nonlinear Resonant Operator and Integral Equations....Pages 128-143
Integral Inclusions....Pages 144-156
Approximation of Solutions of Operator Equations on the Half Line....Pages 157-175
Operator Equations in Banach Spaces Relative to the Weak Topology....Pages 176-190
Stochastic Integral Equations....Pages 191-203
Periodic Solutions for Operator Equations....Pages 204-215
Back Matter....Pages 216-218
Content:
Front Matter....Pages i-ix
Introduction and Preliminaries....Pages 1-13
Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations....Pages 14-36
Solution Sets of Abstract Volterra Equations....Pages 37-45
Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Compact Intervals....Pages 46-64
Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Half-Open Intervals....Pages 65-108
Existence Theory for Nonlinear Nonresonant Operator and Integral Equations....Pages 109-127
Existence Theory for Nonlinear Resonant Operator and Integral Equations....Pages 128-143
Integral Inclusions....Pages 144-156
Approximation of Solutions of Operator Equations on the Half Line....Pages 157-175
Operator Equations in Banach Spaces Relative to the Weak Topology....Pages 176-190
Stochastic Integral Equations....Pages 191-203
Periodic Solutions for Operator Equations....Pages 204-215
Back Matter....Pages 216-218
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