The Conley Index and Rigorous Numerics
The Conley index is a topological invariant of isolated invariant sets, invented by C. Conley and his students in early 70’s. The theory originated from the paper on existence of smooth isolating blocks by Conley and Easton [5]. The first concept of the i
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Series Editors: The Rectors of CISM Sandor Kaliszky - Budapest Mahir Sayir - Zurich Wilhelm Schneider - Wien
The Secretary General of CISM Giovanni Bianchi - Milan
Executive Editor Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES- No. 371
NON LINEAR ANALYSIS AND BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
EDITED BY
F. ZANOLIN UNIVERSITY OF UDINE
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Springer-Verlag Wien GmbH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerch\!.
This volume contains l illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1996 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 1996
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82811-3 DOI 10.1007/978-3-7091-2680-6
ISBN 978-3-7091-2680-6 (eBook)
PREFACE
The theory of ordinary differential equations has received a strong impulse by the introduction of some methods from Nonlinear Analysis (like, e.g., fixed point theorems, degree theory, topological invariants, variational methods) and the study of boundary value problems for ODEs is, at present, a rich area full of significant achievements, both from the theoretical and the applied sides. This volume concerns the study of some boundary value problems for nonlinear ordinary differential equations, using topological or variational methods, with a special emphasis also on the so-called qualitative (or geometric) approach in the theory of ordinary differential equations, making use of a broad collection of techniques coming from Analysis and Topology which are addressed to the study of ODEs. In this book, the study of more classical boundary value problems for ordinary differential equations (like the periodic or the Sturm- Liouville ones) which represent the main interest of a wide number of researchers in the world, is accompanied by the presentation of some recent results dealing with other interesting and more atypical BVPs. In particular, there are new contributions to the study of bounded solutions and to the presentation of some very recent approaches yielding to a rigorous proof of the presence of chaotic motions. The aspect of numerical treat
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