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A perturbation method and the limit-point case of even order symmetric differential expressions

Published online by Cambridge University Press:  14 November 2011

Bernhard Mergler  and
Bernd Schultze
Bernhard Mergler
Affiliation:
Fachbereich 6-Mathematik, Universität Essen-Gesamthochschule, Universitätsstrasse 3, D-4300 Essen 1, West Germany
Bernd Schultze
Affiliation:
Fachbereich 6-Mathematik, Universität Essen-Gesamthochschule, Universitätsstrasse 3, D-4300 Essen 1, West Germany
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Synopsis

We give a new perturbation theorem for symmetric differential expressions (relatively bounded perturbations, with relative bound 1) and prove with this theorem a new limit-point criterion generalizing earlier results of Schultze. We also obtain some new results in the fourth-order case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 121 - 135
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Behnke, H. and Focke, H.. Stability of deficiency indices. Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 119–127.Google Scholar
2Goldberg, S.. Unbounded linear operators (New York: McGraw-Hill, 1966).Google Scholar
3Grudniewicz, C. G. M.. Asymptotic methods for fourth order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 87 (1980), 53–63.Google Scholar
4Hinton, D. B.. Limit-point limit-circle criteria for (py')' + qy = λky. Proc. of the Dundee conference 1974. Lecture Notes in Mathematics 415, 173–183 (Berlin: Springer, 1974).Google Scholar
5Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients. Proc. London Math. Soc. 35 (1977), 496–526.Google Scholar
6Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients (II). Proc. London Math. Soc. 41 (1980), 499–515.Google Scholar
7Niessen, H.-D.. Some perturbation theorems for nullity, deficiency, index and deficiency index, preprint.Google Scholar
8Paris, R. B. and Wood, A. D.. On the L2 nature of solutions of n-th order symmetric differential equations and McLeod's conjecture. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 209–236.Google Scholar
9Paris, R. B. and Wood, A. D.. On a fourth order symmetric differential equation. Quart. J. Math. Oxford 33 (1982), 97–113.Google Scholar
10Schultze, B.. A limit-point criterion for 2n-th order symmetric differential expressions. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 1–12.Google Scholar
11Walker, P. W.. Deficiency indices of fourth order singular differential expressions. J. Differential Equations 9 (1971), 133–140.Google Scholar