On Liapunov’s inequality
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- by Walter Leighton PDF
- Proc. Amer. Math. Soc. 33 (1972), 627-628 Request permission
Abstract:
An elementary proof is given of the Liapunov inequality $\smallint _a^b{p_ + }(x)\;dx > 4/(b - a)$.References
- Stanley B. Eliason, A Lyapunov inequality for a certain second order non-linear differential equation, J. London Math. Soc. (2) 2 (1970), 461–466. MR 267191, DOI 10.1112/jlms/2.Part_{3}.461
- Walter Leighton, Regular singular points in the nonanalytic case; singular functionals, J. Math. Anal. Appl. 28 (1969), 59–76. MR 249719, DOI 10.1016/0022-247X(69)90108-5 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.
- Marston Morse and Walter Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), no. 2, 252–286. MR 1501873, DOI 10.1090/S0002-9947-1936-1501873-7
- Zeev Nehari, On an inequality of Lyapunov, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 256–261. MR 0145149
- William T. Reid, A matrix Liapunov inequality, J. Math. Anal. Appl. 32 (1970), 424–434. MR 268457, DOI 10.1016/0022-247X(70)90308-2
Additional Information
- © Copyright 1972 American Mathematical Society
- 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