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Courant Institute of Mathematical Sciences New York University New York, N.Y. 10012

Lawrence Sirovich

Division of Applied Mathematics Brown University Providence, R.1. 02912

Joseph P. LaSalle

Division of Applied Mathematics Lefschetz Center for Dynamical Systems Providence, R.1. 02912

ADVISORS H. Cabannes University Paris-VI

J. Marsden University of California at Berkeley

J.K. Hale Brown University

G.B. Whitman California Institute of Technology

J. Keller Stanford University

EDITORIAL STATEMENT The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematicalcomputer modelling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books, suitable for the user of mathematics, the mathematician interested in applications, and the student scientist. In particular, this series will provide an outlet for material less formally presented and more anticipatory of needs than finished texts or monographs, yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or lying close to applications. The aim of the series is, through rapid publication in an attractive but inexpensive format, to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction, and unrealistic idealization, but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions to new areas of research , new applications and act as signposts for new directions in the mathematical sciences. This series will often serve as an intermediate stage of the publication of material which, through exposure here, will be further developed and refined. These will appear in conventional format and in hard cover.

MANUSCRIPTS The Editors welcome all inquiries regarding the submission of manuscripts for the series. Final preparation of all manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics, Brown University, Providence, Rhode Island. SPRINGER-VERLAG NEW YORK INC., 175 Fifth Avenue, New York, N. Y. 10010

Applied Mathematical Sciences I Volume 31

William T. Reid

Sturmian Theory for Ordinary Differential Equations

Springer-Verlag New York Heidelberg

Berlin

William T. Reid formerly of the Department of Mathematics University of Oklahoma

Prepared for publication by

John Burns and Terry Herdman Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061/USA

Calvin Ahlbrandt Department of Mathematics University of Missouri Columbia, Missouri 65201/uSA

AMS Subject Classifications: 34-01, 34B25

Library of Congress Cataloging in Publica