Singular Differential and Integral Equations with Applications

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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.