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A limit-point criterion for 2n-th order symmetric differential expressions

Published online by Cambridge University Press:  14 November 2011

Bernd Schultze
Bernd Schultze
Affiliation:
Universität Essen, Fachbereich 6, Mathematik, 43 Essen 1, Germany
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Synopsis

A perturbation theorem for symmetric differential expressions is given and applied to even-order expressions. We assume the coefficients p0(t), pn(t) to be eventually positive and to have real powers of t as dominating terms. Then we are able to admit for the absolute values of the other coefficients a rate of growth depending on the growth of both of the coefficients p0, pn in order to obtain minimal deficiency indices.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 1 - 12
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1.Behncke, H. and Focke, H.. Stability of deficiency indices. Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 119–127.CrossRefGoogle Scholar
2.Evans, W. D. and Zettl, A.. On the deficiency indices of powers of real 2nth-order symmetric differential expressions. J. London Math. Soc. 13 (1976), 543–556.CrossRefGoogle Scholar
3Evans, W. D. and Zettl, A.. Interval limit-point criteria for differential expressions and their powers. J. London Math. Soc. 15 (1977), 119–133.CrossRefGoogle Scholar
4Fedorjuk, M. V.. Asymptotic methods in the theory of one-dimensional singular differential operators. Trans. Moscow Math. Soc. 15 (1966), 296–345.Google Scholar
5Frentzen, H.. A limit-point criterion for real polynomials in symmetric quasi-differential expressions of arbitrary order, to appear.Google Scholar
6Goldberg, S.. Unbounded linear operators (New York: McGraw-Hill, 1966).Google Scholar
7Hinton, D. B.. Limit-point criteria for differential equations. Canad. J. Math. 25 (1972), 293–305.CrossRefGoogle Scholar
8Kato, T.. Perturbation theory for linear operators (Berlin: Springer, 1966).Google Scholar
9Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients. Proc. London Math. Soc. 35 (1977), 496–526.CrossRefGoogle Scholar
10Kauffman, R. M., Read, T. T. and Zettl, A.. The deficiency index problem for powers of ordinary differential expressions. Lecture Notes in Mathematics 621 (Berlin: Springer, 1977).Google Scholar
11Naimark, M. A.. Linear differential operators, Part II (New York: Ungar, 1968).Google Scholar
12Walker, P. W.. Deficiency indices of fourth order singular differential operators. J. Differential Equations 9 (1971), 133–140.CrossRefGoogle Scholar