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...
In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume...
. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five years, the proliferation of the subject is witnessed by hundreds of research articles and several monographs, two International Conferences and numerous Special Sessions, and a new Journal as well as several special issues of existing journals, all devoted to the theme of Difference Equations. Now even those experts who believe in the universality of differential...
. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to o...
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types...
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of appl...
This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point,...
This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In f...
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...
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 ...
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.
In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear,...
In the last century many problems which arose in the science, engineer- ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ- ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis- tence 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...
In the last century many problems which arose in the science, engineer- ing and technology literature involved nonlinear complex phenomena. In many si...
World Scientific Series in Applicable Analysis (WSSIAA) reports new developments of a high mathematical standard and of current interest. Each volume in the series is devoted to mathematical analysis that has been applied, or is potentially applicable to the solution of scientific, engineering, and social problems. This third volume of WSSIAA contains 47 research articles on inequalities by mathematicians from all over the world. It also presents a tribute by R.M. Redheffer to Wolfgang Walter to whom this volume is dedicated - on his 66th birthday.
World Scientific Series in Applicable Analysis (WSSIAA) reports new developments of a high mathematical standard and of current interest. Each volume ...
