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.

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t, y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = 0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In...

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...

This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.

This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis....

This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems. It also provides a detailed account of the current state of the literature on existence theory for ordinary differential equations. Results are presented for finite and semi-infinite intervals. Singularities in both independent and dependent variables are discussed.

Ordinary di?erential equations serve as mathematical models for many exciting "real-world" problems, not only in science and technology, but also in such diverse ?elds as economics, psychology, defense, and demography. Rapid growth in the theory of di?erential equations and in its applications to almost every branch of knowledge has resulted in a continued interest in its study by students in many disciplines. This has given ordinary di?er- tial equations a distinct place in mathematics curricula all over the world and it is now being taught at various levels in almost every institution of...

Fixed point theory has developed into an important field of study in both pure and applied mathematics. This text presents many of the basic techniques and results in this theory. The first three chapters present the basic results and preliminary topics which are later used to develop the presentation.

This book provides a clear exposition of the flourishing field of fixed point theory.