Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-10-04T04:18:29.920Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of the limit-point property of “Kauffman expressions” under relatively bounded perturbations

Published online by Cambridge University Press:  14 November 2011

Bernhard Mergler  and
Bernd Schultze
Bernhard Mergler
Affiliation:
Fachbereich 6-Mathematik, Universität-GHS-Essen, Universitätsstr. 3, 4300 Essen, FRG
Bernd Schultze
Affiliation:
Fachbereich 6-Mathematik, Universität-GHS-Essen, Universitätsstr. 3, 4300 Essen, FRG
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we show that for the whole class of differential expressions in the limit-point case considered by Kauffman in [2], the perturbation theory yields a limit-point criterion for a much wider class of ordinary differential expressions. More general coefficients are admitted which may be eventually negative provided they are “dominated” by some other positive coefficients. This generalises results in [4], [5] and [6].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 1-2 , 1986 , pp. 73 - 89
Copyright
Copyright © Royal Society of Edinburgh 1986

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

1Grudniewicz, C. G. M.. Asymptotic analysis and spectral theory for higher-order differential equations. Ph.D. Thesis, London University, 1980.Google Scholar
2Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients. Proc. London Math. Soc. (3) 35 (1977), 496–526.Google Scholar
3Kwong, M. K. and Zettl, A.. Norm inequalities of product form in weighted L p-spaces. Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 293–307.Google Scholar
4Mergler, B. and Schultze, B.. A perturbation method and the limit-point case of even order symmetric differential expressions. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 121–135.Google Scholar
5Schultze, B.. A limit-point criterion for 2n-th order symmetric differential expressions. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 1–12.Google Scholar
6Schultze, B.. A limit-point criterion for even-order symmetric differential expressions with positive supporting coefficients. Proc. London Math. Soc (3) 46 (1983), 561–576.Google Scholar