The Cauchy Problem for Higher Order Abstract Differential Equations

The main purpose of this book is to present the basic theory and some recent de­ velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . ,

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§ 1. Lecture Notes aim to report new developments - quickly, informally, and at a high level. The texts should be reasonably self-contained and rounded off. Thus they may, and often will, present not only results of the author but also related work by other people. Furthermore, the manuscripts should provide sufficient motivation, examples and applications. This clearly distinguishes Lecture Notes manuscripts from journal articles which normally are very concise. Articles intended for ajournal but too long to be accepted by most journals, usually do not have this "lecture notes" character. For similar reasons it is unusual for Ph. D. theses to be accepted for the Lecture Notes series. § 2. Manuscripts or plans for Lecture Notes volumes should be submitted (preferably in duplicate) either to one of the series editors or to Springer- Verlag, Heidelberg . These proposals are then refereed. A final decision concerning publication can only be made on the basis of the complete manuscript, but a preliminary decision can often be based on partial information: a fairly detailed outline describing the planned contents of each chapter, and an indication of the estimated length, a bibliography, and one or two sample chapters - or a first draft of the manuscript. The editors will try to make the preliminary decision as definite as they can on the basis of the available information. § 3. Final manuscripts should preferably be in English. They should contain at least 100 pages of scientific text and should include - a table of contents; - an informative introduction, perhaps with some historical remarks: it should be accessible to a reader not particularly familiar with the topic treated; - a subject index: as a rule this is genuinely helpful for the reader.

Further remarks and relevant addresses at the back of this book.

Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris

1701

Springer-Verlag Berlin Heidelberg GmbH

Ti-Jun Xiao Jin Liang

The Cauchy Problem for Higher-Order Abstract Differential Equations

Springer

Authors Ti-Jun Xiao Jin Liang Department of Mathematics University of Science and Technology of China Hefei 230026, Anhui People's Republic of China e-mail: [email protected] [email protected]

This work was supported by the National Natural Science Foundation of China Cataloging-in-Publication Data applied for

Die Deutsche Bibliothek - CIP-Einheitsaufnahme

Xiao, Ti-Jun:

The Cauchy problem for rugher order abstract differential equations I TI-Jun Xiao and Jin Liang. (Lecture notes in mathematics; 1701) ISBN 978-3-540-65238-0

Mathematics Subject Classification (1991): Primary: 34010, 47D06; Secondary: 47N20, 35010, 47D09, 93C25, 47F05 ISSN 0075-8434 ISBN 978-3-540-65238-0 ISBN 978-3-540-49479-9 (eBook) DOI 10.1007/978-3-540-49479-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction