Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T09:20:43.510Z Has data issue: false hasContentIssue false
  • English
  • Français

Minors of the wronskian of the differential equation Lny+p(x)y=0

Published online by Cambridge University Press:  14 November 2011

Uri Elias
Uri Elias
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Get access Rights & Permissions [Opens in a new window]

Synopsis

The equation studied here is Lny +p(x)y = 0, where Ln is a disconjugate differential operator and p(x) is of a fixed sign. It is shown that certain minors of the wronskian of this equation satisfy a very similar differential equation Mnz +p(x)z =0. We prove that some properties of the original equation which are essential for oscillation theory are inherited by the solutions of the second one.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 341 - 359
Copyright
Copyright © Royal Society of Edinburgh 1987

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

1Butler, G. J. and Erbe, L. H.. Integral comparison theorems and extremal points linear differential equations. J. Differential Equations 47 (1983), 214–226.CrossRefGoogle Scholar
2Elias, U.. A classification of the solutions of a differential equation according to their asymptotic behaviour. Proc. Roy. Soc. Edinburgh Sect. A 83 (1979), 25–38.CrossRefGoogle Scholar
3Elias, U.. A classification of the solutions of a differential equation according to their behaviour at infinity, II. Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 53–66.CrossRefGoogle Scholar
4Etgen, G. J., Jones, G. D. and Taylor, W. E.. Structure of the solution space of certain linear equations. J. Differential Equations 59 (1985), 229–242.CrossRefGoogle Scholar
5Etgen, G. J., Jones, G. D. and Taylor, W. E.. On the factorization of ordinary linear differential operators. Trans. Amer. Math. Soc. 297 (1986), 717–728.CrossRefGoogle Scholar
6Jones, G. D.. Growth properties of solutions of a linear differential equation (to appear).Google Scholar
7Karlin, S.. Total positivity (Stanford: Stanford University Press, 1968).Google Scholar
8Kim, W. J.. Comparison theorems of Hille-Wintner type for disconjugate differential equations. J. Math. Anal. Appl. 105 (1985), 187–198.CrossRefGoogle Scholar
9Kim, W. J.. Generalized comparison theorems for disfocality types of the equation L ny + py = 0. J. Math. Anal. Appl. 109 (1985), 182–193.CrossRefGoogle Scholar
10Svec, M.. Behaviour of a fourth order self adjoint linear differential equation. Ann. Polon. Math. 42 (1983), 333–344.CrossRefGoogle Scholar