Singular Differential and Integral Equations with Applications (Hardcover)

R.P. Agarwal

ISBN 10: 1402014570 / ISBN 13: 9781402014574

Published by Kluwer Academic Publishers, New York, NY, 2003

About this Item

Hardcover. 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 the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Seller Inventory # 9781402014574

Bibliographic Details

• Title: Singular Differential and Integral Equations with Applications (Hardcover)
• Publisher: Kluwer Academic Publishers, New York, NY
• Publication Date: 2003
• Language: English
• ISBN 10: 1402014570
• ISBN 13: 9781402014574
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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 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 mono­ graph 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. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.

Review

From the reviews:

"In the last years, singular differential and integral equations have assumed an increasing relevance, mainly due to the great variety of problems arisen in sciences, engineering and technology which can be described by such a type of equations. ... This book presents a self-contained up to date survey on the theory available in this setting, together with a wide account to the various applications to physical problems." (Cristina Marcelli, Zentralblatt MATH, Vol. 1055 (6), 2005)