Topics in nonlinear functional analysis. Notes by Ralph A. Artino. (Q2753361)

This is the second edition of the well-known and remarkable book on Nonlinear Analysis. The text is presented unchanged from the first edition except the proof of Proposition 1.7.2. Although the first edition of the book was printed in 1974 one can say that it continues to be actual also this time. Here we recall the contents of the book:NEWLINENEWLINENEWLINEChapter 1 (Topological Approach: Finite Dimensions) in which the Brouwer-Hopf degree theory is presented in detail on the base of Sard's lemma; in the chapter one can find also some information about homotopic theory of continuous mappings between finite-dimensional spaces of different dimensions. Chapter 2 (Topological Degree in Banach Spaces) deals with Leray-Schauder degree theory with some elements of Calculus in Banach Spaces. Chapter 3 (Bifurcation Theory) is devoted to Morse lemma, Krasnosel'ski and Rabinowitz' bifurcation theorems and some their modifications. Chapter 4 (Further Topological Methods) is devoted to some generalizations of Leray-Schauder theory and the theory of framed cobordisms; here the known lectures by J. Ize about application of cohomotopy groups in Nonlinear Analysis are presented. Chapter 5 (Monotone Operators and the Min-Max Theorem) presents also a lecture by N. Bitzenhofer in which it was proved that a monotone set-valued operator in Banach space is in fact single-valued at most point. The last Chapter 6 (Generalized Implicit Functions Theorem) deals with an elegant account to the theorem of Kolmogorov-Arnold-Mozer.NEWLINENEWLINENEWLINEThe book is useful for all specialists in Nonlinear Analysis, first for young mathematicians that, due to this book, can become acquainted with a series of fundamental and brilliant ideas and methods of Nonlinear Analysis.