Language: English
Published by Dordrecht [u.a.] : Kluwer, 2003
ISBN 10: 1402013809 ISBN 13: 9781402013805
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Language: English
Published by Copernicus University Press, Torun, 1998
ISBN 10: 8323109575 ISBN 13: 9788323109570
Seller: killarneybooks, Inagh, CLARE, Ireland
First Edition
Soft cover. Condition: Good. 1st Edition. Paperback, 289 pages, NOT ex-library. A faint beige stain on lower outer page edges externally, also showing - very vaguely - in lower corner of the last and first page inside the book. Else clean and bright with limited wear, firm binding, unmarked text. Free of inscriptions and stamps. -- A collection of advanced research and expository articles in the fields of differential inclusions, topological fixed-point theory, and optimal control. Originating from a 1997 mini-semester hosted by the International Stefan Banach Mathematical Center in Warsaw, in cooperation with the Juliusz Schauder Center for Nonlinear Studies, the volume gathers contributions from leading international mathematicians and emerging scholars, making it a valuable reference point for both established researchers and early-career mathematicians in nonlinear analysis. The book is divided into three thematic sections: differential inclusions, topological methods, and optimal control theory. The topics converge around the role of set-valued and multivalued mappings in modern mathematical systems, exploring how topological and variational methods can be applied to increasingly complex differential problems. The first section deals with the existence, uniqueness, periodicity, and stability of solutions to quasi-linear and semilinear differential inclusions, including works on discontinuous systems (Bressan and Shen), nonlocal boundary value problems (Allegretto and Nistri), and multivalued Nielsen fixed-point theory (Andres, Gorniewicz, and Juzierski). These contributions deepen the theoretical framework for dynamic systems influenced by non-deterministic or discontinuous dynamics. The second section focuses on topological tools and fixed-point theorems, including generalizations of the Borsuk-Ulam theorem (Dzedzej and Izydorek), graph approximations of set-valued maps (Kryszewski), and Leray-Schauder-type theorems with applications to equilibria (Idzik and Park). These provide robust techniques for handling abstract inclusions that arise in infinite-dimensional or nonconvex settings. The third section applies these tools to optimal control problems, Hamilton-Jacobi-Bellman equations, and differential games. Several papers address the uniqueness and regularity of optimal trajectories, shock formation, and state constraints in optimal control theory (Byrnes and Frankowska; Frankowska and Plaskacz). Other contributions explore convex and variational methods, including approximate solutions in the calculus of variations (Moussaoui and Seeger) and conditions for equilibrium in constrained systems. This volume will be especially relevant for researchers interested in the rigorous treatment of dynamical systems governed by multivalued maps, offering a combination of foundational theory, advanced techniques, and applications to physics, mechanics, and control theory.
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Language: English
Published by Springer Netherlands, 2011
ISBN 10: 9048163188 ISBN 13: 9789048163182
Seller: AHA-BUCH GmbH, Einbeck, Germany
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.
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Language: English
Published by Kluwer Academic Publishers, 1999
ISBN 10: 079236001X ISBN 13: 9780792360018
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is an attempt to give a systematic presentation of results and me- ods which concern the xed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to stu- ing topological methods in the xed point theory of multivalued mappings and applications, mainly to di erential inclusions. Thus in Chapter III the approximation (on the graph) method in xed point theory of multivalued mappings is presented. Chapter IV is devoted to the ho- logical methods and contains more general results, e.g. the Lefschetz Fixed Point Theorem, the xed point index and the topological degree theory. In Chapter V applications to some special problems in xed point theory are formulated. Then in the last chapter a direct applications to di erential inclusions are presented. Note that Chapters I and II have an auxiliary character, and only results c- nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the xed point theory. In the last section of our book (see Section 75) we give a bibliographicalguide and also signalsome further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and c- mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. G orka,M.Go rniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is an attempt to give a systematic presentation of results and me- ods which concern the xed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to stu- ing topological methods in the xed point theory of multivalued mappings and applications, mainly to di erential inclusions. Thus in Chapter III the approximation (on the graph) method in xed point theory of multivalued mappings is presented. Chapter IV is devoted to the ho- logical methods and contains more general results, e.g. the Lefschetz Fixed Point Theorem, the xed point index and the topological degree theory. In Chapter V applications to some special problems in xed point theory are formulated. Then in the last chapter a direct applications to di erential inclusions are presented. Note that Chapters I and II have an auxiliary character, and only results c- nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the xed point theory. In the last section of our book (see Section 75) we give a bibliographicalguide and also signalsome further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and c- mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. G orka,M.Go rniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
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Language: English
Published by Walter de Gruyter, Incorporated, 2012
ISBN 10: 3110293447 ISBN 13: 9783110293449
Seller: Majestic Books, Hounslow, United Kingdom
Condition: New. pp. xix + 453 3 Figures.
Language: English
Published by Kluwer Academic Publishers, 1999
ISBN 10: 079236001X ISBN 13: 9780792360018
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