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This book is the first to discuss complementarity theory and variational inequalities using Leray-Schauder type alternatives. Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics. The ideas and method presented in this book may be considered as a starting point for new developments. The book presents a new kind of application for the Leray-Schauder principle.

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Preliminary Notions.- Complementarity Problems and Variational Inequalities.- Leray-Schauder Alternatives.- The Origin of the Notion of Exceptional Family of Elements.- Leray-Schauder Type Alternatives. Existence Theorems.- Infinitesimal Exceptional Family of Elements.- More about the Notion of Exceptional Family of Elements.- Exceptional Family of Elements and Variational Inequalities.

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From the reviews:

"The author of this book is one of the leading specialists in both the theory and applications of complementarity problems ... . The book will be of interest to specialists in applied nonlinear analysis, variational inequalities, complementarity theory, equilibrium theory, and operations research. It may also be used to get a glimpse of the diversity of the directions in which current research in this field is still moving." (Jürgen Appell, Zentralblatt MATH, Vol. 1095 (21), 2006)

"The reviewed monograph studies various classes of complementarity problems and variational inequalities using a unified approach based upon the Leray-Schauder alternative and the concept of an exceptional family of elements (EFE). ... The book is written in a very clear and mathematically rigorous manner, and it is strongly recommended to researchers, postgraduate and graduate students interested in the variational inequality and complementarity problems." (Vyacheslav V. Kalashnikov, Mathematical Reviews, Issue 2007 b)

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