Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions
Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions

Author: T. Yoshizawa

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 240

ISBN-13: 146126376X

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Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.

Almost Periodic Solutions of Impulsive Differential Equations
Almost Periodic Solutions of Impulsive Differential Equations

Author: Gani T. Stamov

Publisher: Springer Science & Business Media

Published: 2012-03-09

Total Pages: 235

ISBN-13: 3642275451

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In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.

Qualitative Problems For Differential Equations And Control Theory
Qualitative Problems For Differential Equations And Control Theory

Author: Constantin Corduneanu

Publisher: World Scientific

Published: 1995-10-06

Total Pages: 345

ISBN-13: 9814549274

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This book contains a collection of articles on the topics mentioned in the title or closely related to them, and is dedicated to Prof Aristide Halanay from the University of Bucharest, Romania, in occasion of his 70th birthday. The authors are in most cases former students of Halanay or research associates from the University of Bucharest, the Mathematical Institute of the Romanian Academy and the Technical University of Bucharest. There are contributions from mathematicians from Finland, Belgium, the United States of America, Morocco, India and Ireland.The topics indicated above are in most cases related to Halanay's work and constitute significant contemporary research items in Applied Mathematics and Engineering. The book is written at research level and is primarily addressing mathematicians interested in the above mentioned areas as well as research engineers. The book will be also useful to graduate students with specialization in the areas listed above.More than 25 authors have contributed to the volume.

Complex Time-Delay Systems
Complex Time-Delay Systems

Author: Fatihcan M. Atay

Publisher: Springer

Published: 2010-03-10

Total Pages: 336

ISBN-13: 3642023290

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One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.

Almost Periodic Solutions of Differential Equations in Banach Spaces
Almost Periodic Solutions of Differential Equations in Banach Spaces

Author: Yoshiyuki Hino

Publisher: CRC Press

Published: 2001-10-25

Total Pages: 276

ISBN-13: 9780415272667

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This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.

nonlinear analysis and applications
nonlinear analysis and applications

Author: Lakshmikantham

Publisher: CRC Press

Published: 2020-11-26

Total Pages: 680

ISBN-13: 1000103609

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This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.