An Introduction to Nonlinear Functional Analysis and Elliptic Problems

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.