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On Liapunov's inequality


Author: Walter Leighton
Journal: Proc. Amer. Math. Soc. 33 (1972), 627-628
MSC: Primary 34D20
DOI: https://doi.org/10.1090/S0002-9939-1972-0291582-4
MathSciNet review: 0291582
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Abstract: An elementary proof is given of the Liapunov inequality $ \smallint _a^b{p_ + }(x)\;dx > 4/(b - a)$.


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  • [1] S. B. Eliason, A Lyapunov inequality for a certain second order non-linear differential equation, J. London Math. Soc. (2) 2 (1970), 461-466. MR 42 #2093. MR 0267191 (42:2093)
  • [2] Walter Leighton, Regular singular points in the nonanalytic case; singular functionals, J. Math. Anal. Appl. 28 (1969), 59-76. MR 40 #2960. MR 0249719 (40:2960)
  • [3] A. M. Ljapunov, Problème générale de la stabilité du movement, Kharkov, 1892; reprint of French transl., Ann. of Math. Studies, no. 17, Princeton Univ. Press, Princeton, N.J., 1947. MR 9, 34.
  • [4] Marston Morse and Walter Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286. MR 1501873
  • [5] Z. Nehari, On an inequality of Lyapunov, Studies in Math. Anal, and Related Topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 256-261. MR 26 #2684. MR 0145149 (26:2684)
  • [6] W. T. Reid, A matrix Liapunov inequality, J. Math. Anal. Appl. 32 (1970), 424-434. MR 42 #3354. MR 0268457 (42:3354)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291582-4
Keywords: Liapunov inequality
Article copyright: © Copyright 1972 American Mathematical Society

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