This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder's. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.
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"The book leaves an overall pleasant impression. The contents are very well organized and well written. It is a valuable contribution to the literature on a class of methods of nonlinear analysis, providing an overview of classical techniques while introducing significant new ones." (Luis Fernando Sanchez Rodrigues, Mathematical Reviews, April, 2024)
"The monograph is perfectly organized and very well written. It provides a detailed presentation and insight on this new extension of the degree theory and illustrates the applicability of this tool in several problems. For these reasons, this book is suitable for researchers willing to learn more on this interesting topic." (Guglielmo Feltrin, zbMATH 1505.47003, 2023)
"The monograph is perfectly organized and very well written. It provides a detailed presentation and insight on this new extension of the degree theory and illustrates the applicability of this tool in several problems. For these reasons, this book is suitable for researchers willing to learn more on this interesting topic." (Guglielmo Feltrin, zbMATH 1505.47003, 2023)