Details

Autor(en) / Beteiligte

• Andres, Jan
• Górniewicz, Lech

Titel

Topological Fixed Point Principles for Boundary Value Problems [Elektronische Ressource]

Ist Teil von

• Topological Fixed Point Theory and Its Applications : 1

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

2003

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 topological fixed point theory in non-metric spaces. Although the theoretical material was tendentially selected with respect to applications, we wished to have a self-consistent text (see the scheme below). Therefore, 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 familiar in some related sections with the notions like the Bochner integral, the Aumann 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