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Existence of conjugate points for self-adjoint linear differential equations

Published online by Cambridge University Press:  14 November 2011

Ondřej Došlý
Ondřej Došlý
Affiliation:
Department of Mathematics, J. E. Purkyně University, Janáčkovo náměstí 2a, 662 95 Brno, Czechoslovakia
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Synopsis

The conjecture of Muller-Pfeiffer [4] concerning the oscillation behaviour of the differential equation (–l)n(p(x)y(n))(n) + q(x)y = 0 is proved, and a similar conjecture concerning the more general differential equation ∑nk=0(−l)k(Pk(x)y(k)(k + q(x)y= 0 is formulated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 1-2 , 1989 , pp. 73 - 85
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Ahlbrandt, C. D., Hinton, D. B. and Lewis, R. T.. The effect of variable change on oscillation and disconjugacy criteria with application to asymptotic and spectral theory. J. Math. Anal. Appl. 81 (1981), 234–277.CrossRefGoogle Scholar
2Coppel, W. A.. Disconjugacy, Lecture Notes in Math. 220 (Berlin: Springer, 1971).CrossRefGoogle Scholar
3Hartman, P.. Ordinary Differential Equations (New York: John Wiley, 1964).Google Scholar
4Müller-Pfeiffer, E.. Existence of conjugate points for second and fourth order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 281–291.CrossRefGoogle Scholar
5Müller-Pfeiffer, E.. An oscillation theorem for certain self-adjoint differential equations. Math. Nachr. 108 (1982), 79–92.CrossRefGoogle Scholar
6Reid, W. T.. Ordinary Differential Equations (New York: John Wiley, 1971).Google Scholar
7Swanson, C. A.. Oscillation and Comparison Theory for Linear Differential Equations (New York: Academic Press, 1968).Google Scholar