Topological Fixed Point Principles for Boundary Value Problems (Topological Fixed Point Theory and Its Applications, 1)

Andres, J.; Górniewicz, Lech

ISBN 10: 1402013809 / ISBN 13: 9781402013805

Edité par Springer, 2003

A propos de cet article

In.

N° de réf. du vendeur ria9781402013805_new

Détails bibliographiques

• Titre: Topological Fixed Point Principles for Boundary Value Problems (Topological Fixed Point Theory and Its Applications, 1)
• Éditeur: Springer
• Date de parution: 2003
• Langue: anglais
• ISBN à 10 chiffres: 1402013809
• ISBN à 13 chiffres: 9781402013805
• Reliure: Couverture rigide
• État de l'article: New

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

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.