An Introduction to Nonlinear Functional Analysis and Elliptic Problems This self contained textbook provides the basic abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method this comprehensive text displays how various approaches can easily be applied to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems is divided into two parts: the first discusses key results such as the Banach contraction principle a fixed point theorem for increasing operators local and global inversion theory Leray–Schauder degree critical point theory and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems. The exposition is driven by numerous prototype problems and exposes a variety of approaches to solving them. Complete with a preliminary chapter an appendix that includes further results on weak derivatives and chapter by chapter exercises this book is a practical text for an introductory course or seminar on nonlinear functional analysis. Notation Preliminaries Some Fixed Point Theorems Local and Global Inversion Theorems Leray Schauder Topological Degree An Outline of Critical Points Bifurcation Theory Elliptic Problems and Functional Analysis Problems with A Priori Bounds Asymptotically Linear Problems Asymmetric Nonlinearities Superlinear Problems Quasilinear Problems Stationary States of Evolution Equations Appendix A Sobolev Spaces Exercises Index Bibliography.