Topological Fixed Point Principles for Boundary Value Problems

2003. Auflage 2003
ISBN: 978-1-4020-1380-5
Verlag: Springer

Buch, Englisch, Band 1, 761 Seiten, Format (B × H): 165 mm x 239 mm, Gewicht: 1497 g

Reihe: Topological Fixed Point Theory and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Andres, J.

Górniewicz, Lech

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Topologie Analytische Topologie

Inhaltsverzeichnis

I Theoretical background.- II General principles.- III Application to differential equations and inclusions.- Appendices.- A.1. Almost-periodic single-valued and multivalued functions.- A.2. Derivo-periodic single-valued and multivalued functions.- A.3. Fractals and multivalued fractals.- References.