This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
Overview. Theorems of Leray-Schauder Type for Contractions. Continuation Theorems for Nonexpansive Maps. Theorems of Leray-Schauder Type for Accretive Maps. Continuation Theorems Involving Compactness. Applications to Semilinear Elliptic Problems. Theorems of Leray-Schauder Type for Coincidences. Theorems of Selective Continuation. The Unified Theory. Multiplicity. Local Continuation Theorems.