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An integral inequality with an application to ordinary differential operators*

  • W. N. Everitt (a1)

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.

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References

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1Beckenbach, E. F. and Bellman, R.Inequalities (Berlin: Springer, 1961).
2Everitt, W. N.On the spectrum of a second-order linear differential equation with a p-integrable coefficient. Applicable Anal. 2 (1972), 143160.
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4Glazman, I. M.Direct methods for the qualitative spectral analysis of singular differential operators (Jerusalem: Israel Program Sci. Transl., 1965).
5Goldberg, S.Unbounded linear operators (New York: McGraw-Hill, 1966).
6Hardy, G. H., Littlewood, J. E. and Polya, G.Inequalities (Cambridge: University Press, 1934).
7Hellwig, G.Differential operators of mathematical physics (London: Addison-Wesley, 1967).
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9Mitrinović, D. S.Analytic inequalities (Berlin: Springer, 1970).
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12Titchmarsh, E. C.Eigenfunction expansions associated with second-order differential equations I (Oxford: University Press, 1962).

An integral inequality with an application to ordinary differential operators*

  • W. N. Everitt (a1)

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