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A second order Dirichlet differential expression that is not bounded below

Published online by Cambridge University Press:  14 November 2011

Man Kam Kwong
Man Kam Kwong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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Synopsis

We give in this note a second order singular differential expression of the form Lf = −f″ + qf on [0, ∞) that satisfies the Dirichlet condition but that is not bounded below.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 39 - 43
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Amos, R. J. and Everitt, W. N.. On a quadratic integral inequality. Proc. Roy. Soc. Edinb. Sect. A 78 (1978), 241–256.CrossRefGoogle Scholar
2Bradley, J. S. and Everitt, W. N.. Inequalities associated with regular and singular problems in the calculus of variations. Trans. Amer. Math. Soc. 182 (1973), 303–321.CrossRefGoogle Scholar
3Bradley, J. S. and Everitt, W. N.. A singular integral inequality on a bounded interval. Proc. Amer. Math. Soc. 61 (1976), 29–35.CrossRefGoogle Scholar
4Kalf, H.. Remarks on some Dirichlet type results for semibounded Sturm-LiouviUe operators. Math. Ann. 210 (1974), 197–205.CrossRefGoogle Scholar
5Kato, T.. Perturbation Theory for Linear Operators (Berlin: Springer, 1966).Google Scholar
6Rellich, F.. Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung. Math. Ann. 122 (1951), 343–368.CrossRefGoogle Scholar
7Wintner, A.. A criterion of oscillatory stability. Quart. Appl. Math. 7 (1949), 115–117.CrossRefGoogle Scholar