Methods of Nonlinear Analysis / Birkhäuser Advanced Texts Basler Lehrbücher (PDF)

From the reviews:

“This monograph contains old and new basic results from a significant part of the modern Nonlinear Analysis. … The book is well written and contains a wealth of material. … The book is carefully written, the style is informal, and the arguments are clear. It is a delightful read. … This book is recommended to researchers in Applied Mathematics who study various linear and nonlinear phenomena but it may be also useful and comprehensive for a broader community of mathematicians, physicists, and engineers.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1176, 2010)

“The book covers a number of important methods in nonlinear analysis on a graduate level. … Each chapter consists of a self-contained introduction and ends with a number of appendices treating more advanced topics. The intention of the authors is to provide a well-motivated introduction to these topics and to demonstrate the usefulness of the derived methods in nontrivial applications, a task in which they succeed remarkably well.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)

“This book offers a self-contained introduction to certain central topics of functional analysis and topology for advanced undergraduate and graduate students. … the clear and self-contained style recommend the book for self-study, offering a quick introduction to a number of central notions of functional analysis and topology. A large number of exercises and historical remarks add to the pleasant overall impression the book leaves.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (3), March, 2009)