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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Liapunov functions and $L^{p}$ solutions of differential equations
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by Aaron Strauss PDF
Trans. Amer. Math. Soc. 119 (1965), 37-50 Request permission
References
  • H. A. Antosiewicz, A survey of Lyapunov’s second method, Contributions to the theory of nonlinear oscillations, Vol. IV, Annals of Mathematics Studies, no. 41, Princeton University Press, Princeton, N.J., 1958, pp. 141–166. MR 0102643
  • Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 16, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0151677, DOI 10.1007/978-3-662-00105-9
  • Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
  • Wolfgang Hahn, Theory and application of Liapunov’s direct method, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. English edition prepared by Siegfried H. Lehnigk; translation by Hans H. Losenthien and Siegfried H. Lehnigk. MR 0147716
  • N. N. KrasovskiÄ­, Stability of motion. Applications of Lyapunov’s second method to differential systems and equations with delay, Stanford University Press, Stanford, Calif., 1963. Translated by J. L. Brenner. MR 0147744
  • J. J. Levin, On the global asymptotic behavior of nonlinear systems of differential equations, Arch. Rational Mech. Anal. 6 (1960), 65–74 (1960). MR 119525, DOI 10.1007/BF00276154
  • J. J. Levin and J. A. Nohel, Global asymptotic stability for nonlinear systems of differential equations and applications to reactor dynamics, Arch. Rational Mech. Anal. 5 (1960), 194–211 (1960). MR 119524, DOI 10.1007/BF00252903
    • A. Lyapounov, ProblĂšme gĂ©nĂ©ral de la stabilitĂ© du mouvement, Annals of Mathematics Studies No. 17, Princeton Univ. Press, Princeton, N. J., 1949.
  • J. L. Massera, On Liapounoff’s conditions of stability, Ann. of Math. (2) 50 (1949), 705–721. MR 35354, DOI 10.2307/1969558
    • K. P. Persidskii, Theory of stability of integrals of a system of differential equations, Izvestia, Gostehizdat, Vol. 8, 1936-1937.
  • Taro Yoshizawa, On the non-linear differential equation, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 28 (1954), 133–141. MR 65732, DOI 10.1215/kjm/1250777428
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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 119 (1965), 37-50
  • MSC: Primary 34.51
  • DOI: https://doi.org/10.1090/S0002-9947-1965-0178203-7
  • MathSciNet review: 0178203