R.P. Agarwal - Böcker

In 1960 the Polish mathematician Zdzidlaw Opial (1930-1974) published an inequality involving integrals of a function and its derivative. This book offers a systematic and up-to-date account of developments in Opial-type inequalities. It presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.

This monograph is a collection of the results the authors have obtained on difference equations and inequalities. In the last few years this discipline has gone through such a dramatic development that it is no longer feasible to present an exhaustive survey of all research. However, this volume offers a representative overview of the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject.

This monograph presents an up-to-date account of the theory of right focal point boundary value problems for differential and difference equations. Topics include existence and uniqueness, Picard's method, quasilinearisation, necessary and sufficient conditions for right disfocality, right and eventual disfocalities, Green's functions, monotone convergence, continuous dependence and differentiation with respect to boundary values, infinite interval problems, best possible results, control theory methods, focal subfunctions, singular problems, and problems with impulse effects. This work should be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

In analyzing non-linear phenomena, many mathematical models give rise to problems for which only non-negative solutions make sense. This volume reflects some of the major advances in the field as well as the diversity of the subject. This text will be of interest to graduate students and researchers in mathematical analysis and its applications, whose work involves ordinary differential equations, finite differences and integral equations.

This text reviews material from more than 300 publications on the oscillation theory of difference and functional differential equations of various types. For difference equations, a large number of new concepts is explained and supported by theoretical developments. For differential equations, simplified versions of several new integral criteria for oscillations are presented. Proofs which illustrate the various strategies and ideas involved are given. This book should be a stimulus to the further development of the theory. It should be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

This monograph is a cumulation mainly of the author's research over a period of more than 10 years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is the illustration of almost all results with examples. This book should turn out to be a stimulus to the further development of the theory.

In this monograph, the authors present a systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. A feature of this monograph is the illustration of several results with examples of interest in 2003. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

In the 20th century many problems which arose in the science, engineering and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to: ordinary differential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions; and Volterra and Fredholm type integral equations. As one might expect general existence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This monograph presents an up to date account of the literature on singular problems. One of our aims also is to present theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems.An important feature of this book is that it illustrates how easily the theory can be applied to discuss many real-world examples of contemporary interest.

In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.

This monograph is a collection of the results the authors have obtained on difference equations and inequalities. In the last few years this discipline has gone through such a dramatic development that it is no longer feasible to present an exhaustive survey of all research. However, this state-of-the-art volume offers a representative overview of the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject. Audience: This book will be of interest to graduate students and researchers in mathematical analysis and its applications, concentrating on finite differences, ordinary and partial differential equations, real functions and numerical analysis.

This monograph presents an up-to-date account of the theory of right focal point boundary value problems for differential and difference equations. Topics include existence and uniqueness, Picard's method, quasilinearisation, necessary and sufficient conditions for right disfocality, right and eventual disfocalities, Green's functions, monotone convergence, continuous dependence and differentiation with respect to boundary values, infinite interval problems, best possible results, control theory methods, focal subfunctions, singular problems, and problems with impulse effects. Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense. In the last few years this discipline has grown dramatically. This state-of-the-art volume offers the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject. Audience: This volume will be of interest to graduate students and researchers in mathematical analysis and its applications, whose work involves ordinary differential equations, finite differences and integral equations.

This book reviews material from more than three hundred publications on the oscillation theory of difference and functional differential equations of various types. For difference equations, a large number of new concepts are explained and supported by interesting theoretical developments. For differential equations, simplified versions of several new integral criteria for oscillations are presented. Proofs which illustrate the various strategies and ideas involved are given. This book should be a stimulus to the further development of the theory. Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory.This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

This monograph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest.

Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom­ ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

Nonlinear Analysis and Applications is dedicated to Professor V. Lakshmikantham on the occasion of his 80th birthday. The volumes consist of 45 research papers from distinguished experts from a variety of research areas. Topics include monotonicity and compact methods, blow up and global existence for hyperbolic problems, dynamic systems on time scales, maximum monotone mappings, fixed point theory, quasivalued elliptic problems including mixed BVP's, impulsive and evolution inclusions, iterative processes, Morse theory, hemivariational inequalities, Navier-Stokes equations, multivalued BVP's, various aspects of control theory, integral operators, semigroup theories, modelling of real world phenomena, higher order parabolic equations, invariant measures, superlinear problems and operator equations.