Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-02T00:01:02.877Z Has data issue: false hasContentIssue false

Limit-point criteria for polynomials in a non-oscillatory expression*

Published online by Cambridge University Press:  14 February 2012

T. T. Read
Affiliation:
Department of Mathematics, University of Dundee

Synopsis

Several criteria are given for some or all polynomials in an expression M(y) = –(py′)′+qy which is non-oscillatory on (0, ∞) to be limit-point. One of these states that if M is non-oscillatory and , then every polynomial in M is limit-point.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1976

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

1Brinck, I.. Self-adjointness and spectra of Sturm-Liouville operators. Math. Scand. 7 (1959), 219239.CrossRefGoogle Scholar
2Chaudhuri, J. and Everitt, W. N.. On the square of a formally self-adjoint differential expression. J. London Math. Soc. 1 (1969), 661673.CrossRefGoogle Scholar
3Coppel, W. A.. Disconjugacy. Lecture notes in mathematics 220 (Berlin: Springer, 1971).Google Scholar
4Dunford, N. and Schwartz, J. T.. Linear operators, II (New York: Interscience, 1963).Google Scholar
5Eastham, M. S. P.. Limit-circle differential expressions of the second order with an oscillating coefficient. Quart J. Math. Oxford Ser. 24 (1973), 257263.CrossRefGoogle Scholar
6Everitt, W. N. and Giertz, M.. On some properties of the powers of a formally self-adjoint differential expression. Proc. London Math. Soc. 24 (1972), 149170.Google Scholar
7Everitt, W. N. and Giertz, M.. On the integrable-square classification of ordinary symmetric differential expressions. J. London Math. Soc. 10 (1975), 417426.Google Scholar
8Hartman, P.. Differential equations with non-oscillatory eigenfunctions. Duke Math. J. 15 (1948), 697709.Google Scholar
9Kauffman, R. M.. Polynomials and the limit point condition. Trans. Amer. Math. Soc. 201 (1975), 347366.CrossRefGoogle Scholar
10Naimark, M. A.. Linear differential operators, II (New York: Ungar, 1968).Google Scholar
11Read, T. T.. Bounds and quantitative comparison theorems for nonoscillatory second order differential equations. Pacific J. Math., to appear.Google Scholar
12Read, T. T.. A limit-point criterion for expressions with oscillatory coefficients. Pacific J. Math., to appear.Google Scholar
13Read, T. T.. On the limit point condition for polynomials in a second order differential expression. J. London Math. Soc. 10 (1975), 357366.Google Scholar