Andrzej Granas - Böcker

-Felix Browder, Rutgers University"The theory of Fixed Points is one of the most powerful tools of modern mathematics. Not only is it used on a daily basis in pure and applied mathematics, but it also serves as a bridge between Analysis and Topology, and provides a very fruitful area of interaction between the two. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications."-Haim Brezis, Universite Pierre et Marie Curie"In this monograph, no effort has been spared, even to the smallest detail, be it mathematical, historical or bibliographical. In particular, the necessary background materials are generously provided for non-specialists. In fact, the book could even serve as an introduction to algebraic topology among others. It is certain that the book will be a standard work on Fixed Point Theory for many years to come."-Isaac Namioka, University of WashingtonThis monograph gives a carefully worked out account of the most basic principles and applications of the theory of fixed points.Until now, a treatment of many of the discussed topics has been unavailable in book form. The presentation is self-contained and is accessible to a broad spectrum of readers. The main text is complemented by numerous exercises, detailed comments, and a comprehensive bibliography. The first part of this book is based on "Fixed Point Theory I" which was published by PWN, Warsaw in 1982. The second part follows the outline conceived by Andrzej Granas and the late James Dugundji.

The main topics covered in this text, which contains the proceedings of a NATO ASI conference held in Montreal, are: non-smooth critical point theory; second order differential equations on manifolds and forced oscillations; topological approach to differential inclusions; periodicity of singularly perturbed delay equations; existence, multiplicity and bifurcation of solutions of nonlinear boundary value problems; some applications of the topological degree to stability theory; bifurcation problems for semilinear elliptic equations; ordinary differential equations in Banach spaces; and the centre manifold technique and complex dynamics of reaction diffusion equations.

The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non­ linear functional analysis, emphasizing developments related to the Leray­ Schauder theory. Using for the most part geometric methods, our study cen­ ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe­ matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre­ supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer­ cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.