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An integral inequality with an application to ordinary differential operators*

Published online by Cambridge University Press:  14 November 2011

W. N. Everitt
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

This paper is concerned with integral inequalities of the form

where p, q are real-valued coefficients, with p and w non-negative, on the compact interval [a, b] and D is a linear manifold of functions so chosen that all three integrals are absolutely convergent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 35 - 44
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Beckenbach, E. F. and Bellman, R.Inequalities (Berlin: Springer, 1961).CrossRefGoogle Scholar
2Everitt, W. N.On the spectrum of a second-order linear differential equation with a p-integrable coefficient. Applicable Anal. 2 (1972), 143–160.CrossRefGoogle Scholar
3Everitt, W. N., Giertz, M. and Weidmann, J.Some remarks on a separation and limit-point criterion of second-order, ordinary differential expressions. Math. Ann. 200 (1973), 335–346.CrossRefGoogle Scholar
4Glazman, I. M.Direct methods for the qualitative spectral analysis of singular differential operators (Jerusalem: Israel Program Sci. Transl., 1965).Google Scholar
5Goldberg, S.Unbounded linear operators (New York: McGraw-Hill, 1966).Google Scholar
6Hardy, G. H., Littlewood, J. E. and Polya, G.Inequalities (Cambridge: University Press, 1934).Google Scholar
7Hellwig, G.Differential operators of mathematical physics (London: Addison-Wesley, 1967).Google Scholar
8Ince, E. L.Ordinary differential equations (London: Longmans, 1926).Google Scholar
9Mitrinović, D. S.Analytic inequalities (Berlin: Springer, 1970).CrossRefGoogle Scholar
10Naimark, M. A.Linear differential operators II (New York: Ungar, 1968).Google Scholar
11Rellich, F.Halbschränkte gewöhnliche Differentialoperatoren zweiter Ordnung. Math. Ann. 122 (1951), 343–368.CrossRefGoogle Scholar
12Titchmarsh, E. C.Eigenfunction expansions associated with second-order differential equations I (Oxford: University Press, 1962).Google Scholar