Non-Oscillation Domains of Differential Equations with Two Parameters
This research monograph is an introduction to single linear differential equations (systems) with two parameters and extensions to difference equations and Stieltjes integral equations. The scope is a study of the values of the parameters for which the eq
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1338 Angelo B. Mingarelli S. Gotskalk Halvorsen
Non-Oscillation Domains of Differential Equations with Two Parameters
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann
1338 Angelo B. Mingarelli S. Gotskalk Halvorsen
Non-Oscillation Domains of Differential Equations with Two Parameters
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Authors
Angelo B. Mingarelli Department of Mathematics, University of Ottawa Ottawa, Ontario, Canada, K 1N6N5 S. Gotskalk Halvorsen Department of Mathematics, University of Trondheim NTH Trondheim, Norway
Mathematics Subject Classification (1980): Primary: 34A30, 34C 10,45005 Secondary: 34C 15, 39A 10, 39A 12 ISBN 3-540-50078-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-50078-2 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr, 2146/3140-543210
... Et si illa oblita fuerit, ego tamen non obliviscar tui, Ecce in manibus mei descripsi teo ( Is. 49, 15-16)
Per Felice, Angelino ,Dulcineo e Michelino In memoriam
Preface The aim of these notes is to study the large-scale structure of the non-oscillation and disconjugacy domains of second order linear differential equations with two parameters and various extensions of the latter. We were heavily influenced in this endeavor by a paper of Markus and Moore [Mo.2J. The applications to Hill's equation, Mathieu's equation, along with their discrete analogs, motivated many of the questions, some resolved, and some unresolved, in this work. As we wished to consider linear systems of second order differential equations, Sturm ian methods had to be avoided. Thus we chose to base the theory essentially on variational methods - For this reason many of the results herein will have analogs in higher dimensions (e.g., for Schrodinger operators) although we have not delved into this matter here. The first author (ABM) wishes to thank the Department of Mathematics, University of Trondheim - N.T.H., for making possible his visit there during September 1984 and for the kind hospitality rendered while there. He also wishes to acknowledge with thanks the support of the Natural Sciences and Engineering Research Council of Canada in the form of a research grant and a University Research Fellowship. Finally, he acknowledges with thanks the assistance of France Prud'Homme and Manon G
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