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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."
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."
This book provides a clear exposition of the flourishing field of
fixed point theory. Starting from the basics of Banach's
contraction theorem, most of the main results and techniques are
developed: fixed point results are established for several classes
of maps and the three main approaches to establishing continuation
principles are presented. The theory is applied to many areas of
interest in analysis. Topological considerations play a crucial
role, including a final chapter on the relationship with degree
theory. Researchers and graduate students in applicable analysis
will find this to be a useful survey of the fundamental principles
of the subject. The very extensive bibliography and close to 100
exercises mean that it can be used both as a text and as a
comprehensive reference work, currently the only one of its type.
This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.
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