Existence Theory for Nonlinear Integral and Integrodifferential Equations

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.