Topological Fixed Point Principles for Boundary Value Problems

J. Andres

ISBN 10: 1402013809 / ISBN 13: 9781402013805

Published by Springer Jul 2003, 2003

About this Item

Neuware - Our book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topo logical fixed point theory in non-metric spaces. Although the theoretical material was tendentially selected with respect to ap plications, we wished to have a self-consistent text (see the scheme below). There fore, we supplied three appendices concerning almost-periodic and derivo-periodic single-valued {multivalued) functions and (multivalued) fractals. The last topic which is quite new can be also regarded as a contribution to the fixed point theory in hyperspaces. Nevertheless, the reader is assumed to be at least partly famil iar in some related sections with the notions like the Bochner integral, the Au mann multivalued integral, the Arzela-Ascoli lemma, the Gronwall inequality, the Brouwer degree, the Leray-Schauder degree, the topological (covering) dimension, the elemens of homological algebra, . Otherwise, one can use the recommended literature. Hence, in Chapter I, the topological and analytical background is built. Then, in Chapter II (and partly already in Chapter I), topological principles necessary for applications are developed, namely: the fixed point index theory (resp. the topological degree theory), the Lefschetz and the Nielsen theories both in absolute and relative cases, periodic point theorems, topological essentiality, continuation-type theorems.

Seller Inventory # 9781402013805

Bibliographic Details

• Title: Topological Fixed Point Principles for Boundary Value Problems
• Publisher: Springer Jul 2003
• Publication Date: 2003
• Language: English
• ISBN 10: 1402013809
• ISBN 13: 9781402013805
• Binding: Buch
• Condition: Neu
• Dimensions: 239W x 165H x 36D millimeters 239 millimeters width by 165 millimeters height by 36 millimeters depth
• Weight: 1497 grams

About this title

Synopsis

The book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topological fixed point theory in non-metric spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Therefore, three appendices concerning almost-periodic and derivo-periodic single-valued (multivalued) functions and (multivalued) fractals are supplied to the main three chapters.

Review

From the reviews:

"This book is the most complete and well written text so far on the applications of topological fixed point principles to boundary value problems for ordinary differential equations and differential inclusions. It is a unique monograph dealing with topological fixed point theory in the framework of non-metric spaces, and part of the material focuses on recent results of one author, or both of them." -- MATHEMATICAL REVIEWS

"The monograph is devoted to the topological fixed point theory ... . The book is self-contained and every chapter concludes by a section of Remarks and Comments ... . I believe that this monumental monograph will be extremely useful to postgraduates students and researchers in topological fixed point theory nonlinear analysis, nonlinear differential equations and inclusions ... . This book should stimulate a great deal of interest and research in topological methods in general and in their applications in particular." (Radu Precup, Studia universitatis Babes-Bolyai Mathematica, Vol. XLIX (1), 2004)