Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend
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Valery V. Kozlov Stanislav D. Furta
Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
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Valery V. Kozlov Steklov Mathematical Institute Russian Academy of Sciences Moscow Russia
Stanislav D. Furta Faculty for Innovative and Technological Business Russian Academy of National Economy and Public Administration Moscow Russia
Translation of the 2nd Russian original edition entitled “Asimptotiki reshenij sil’no nelinejnykh sistem differentsial’nykh uravnenij”, published jointly by RCD (Regular and Chaotic Dynamics), Izhevsk, and IKI (Institut Kompyuternykh Issledovanij), Moscow, in 2009 ISSN 1439-7382 ISBN 978-3-642-33816-8 ISBN 978-3-642-33817-5 (eBook) DOI 10.1007/978-3-642-33817-5 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012954017 Mathematics Subject Classification (2010): 34D05, 34D XX c Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Translator’s Note
The translator has worked with the theory of differential equations and its applications for many years, and yet the translation of the present book presented significant challenges, for from the outset new territory needed to be explored
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