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OSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

Part of: Qualitative theory

Published online by Cambridge University Press:  09 February 2009

MARTIN CHUAQUI ,
PETER DUREN ,
BRAD OSGOOD  and
DENNIS STOWE
MARTIN CHUAQUI
Affiliation:
Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile (email: mchuaqui@mat.puc.cl)
PETER DUREN*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA (email: duren@umich.edu)
BRAD OSGOOD
Affiliation:
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA (email: osgood@ee.stanford.edu)
DENNIS STOWE
Affiliation:
Department of Mathematics, Idaho State University, Pocatello, ID 83204, USA (email: stowdenn@isu.edu)
*
✉For correspondence; e-mail: duren@umich.edu
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Abstract

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In this note we study the zeros of solutions of differential equations of the form u′′+pu=0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given.

Keywords

linear differential equationszeros of solutionsoscillationrelative convexitySturm comparison theoremSchwarzian derivativeunivalence

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 161 - 169
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The authors are supported by Fondecyt Grant #1071019.

References

[1] Birkhoff, G. and Rota, G.-C., Ordinary Differential Equations, 4th edn (Wiley, New York, 1989).Google Scholar
[2] Chuaqui, M., Duren, P. and Osgood, B., ‘Schwarzian derivative criteria for valence of analytic and harmonic mappings’, Math. Proc. Cambridge Philos. Soc. 143 (2007), 473–486.CrossRefGoogle Scholar
[3] Hartman, P., Ordinary Differential Equations, 2nd edn (Birkhäuser, Boston, MA, 1982).Google Scholar
[4] Hille, E., Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA, 1969).Google Scholar
[5] Kamke, E., Differentialgleichungen: Lösungsmethoden und Lösungen, Band 1: Gewöhnliche Differentialgleichungen (3 Auflage, Becker & Erler, Leipzig, 1944) (reprinted by Chelsea, New York, 1948).Google Scholar
[6] Nehari, Z., ‘The Schwarzian derivative and schlicht functions’, Bull. Amer. Math. Soc. 55 (1949), 545–551.CrossRefGoogle Scholar
[7] Nehari, Z., ‘Some criteria of univalence’, Proc. Amer. Math. Soc. 5 (1954), 700–704.CrossRefGoogle Scholar
[8] Nehari, Z., ‘Univalence criteria depending on the Schwarzian derivative’, Illinois J. Math. 23 (1979), 345–351.CrossRefGoogle Scholar