Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T08:27:37.507Z Has data issue: false hasContentIssue false
  • English
  • Français

4.—An Algorithm for the Construction of all Disconjugate Operators.*†

Published online by Cambridge University Press:  14 February 2012

Anton Zettl
Anton Zettl
Affiliation:
Department of Mathematics, University of Dundee and Northern Illinois University, De Kalb, Illinois.
Get access Rights & Permissions [Opens in a new window]

Synopsis

A differential operator (1) Ly = y(n) + an-1(t)y(n-1) +…+ao(t)y is said to be disconjugate on an interval I if every non-trivial solution of Ly = 0 has less than n zeros on I, multiple zeros being counted according to their multiplicity. An algorithm for the construction of disconjugate operators of type (1) is given here. All such operators are obtained at least in the case when the interval I is open or compact.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 1 , 1976 , pp. 33 - 40
Copyright
Copyright © Royal Society of Edinburgh 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Coppel, W. A.. Disconjugacy. Lecture Notes in Mathematics 220 (Berlin: Springer, 1971).Google Scholar
2Frobenius, G.. Über die Determinante mehrerer Funktionen einer Variablen.J. Reine Angew. Math. 77 (1874), 245–257.Google Scholar
3Libri, G.. Mémoire sur la résolution des équations algébriques dont les racines ont entre elles un rapport donné, et sur l'intégration des équations différentielles linéares dont les intégrales paticulières peuvent sexprimer les unes par les autres. J. Reine Angew. Math. 10 (1833), 167–194.Google Scholar
4Mammana, G.. Decomposizione delle espressioni differenzioli lineari omogenee in prodotto di fattori simbolici e applicazion relativa allo studio delle equazioni differnenzi ali lineari. Math. Z. 33(1931), 186–231.CrossRefGoogle Scholar
5Polya, G.. On the mean-value theorem corresponding to a given linear homogeneous differential equation. Trans. Amer. Math. Soc. 24 (1924), 312–324.Google Scholar
6Sturm, C.. Sur les équations différentielles linéares du second ordre.. J. Math. Pures Appl. 1 (1836), 106–186.Google Scholar
7Swanson, C. A.. Comparison and oscillation theory of linear differential equations (New York: Academic Press, 1968).Google Scholar