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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
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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

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References

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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