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.

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.