Singular Differential and Integral Equations with Applications eBook

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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.

This is a digital product.

Singular Differential and Integral Equations with Applications is written by R. P. Agarwal; Donal O’Regan and published by Springer. The Digital and eTextbook ISBNs for Singular Differential and Integral Equations with Applications are 9789401730044, 9401730040 and the print ISBNs are 9789048163564, 9048163560. Additional ISBNs for this eTextbook include 9781402014574.