Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Liapunov functions and $ L\sp{p}$ solutions of differential equations


Author: Aaron Strauss
Journal: Trans. Amer. Math. Soc. 119 (1965), 37-50
MSC: Primary 34.51
MathSciNet review: 0178203
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] 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 (21 #1432)
  • [2] Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Bd. 16, Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0151677 (27 #1661)
  • [3] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338 (16,1022b)
  • [4] Wolfgang Hahn, Theory and application of Liapunov’s direct method, English edition prepared by Siegfried H. Lehnigk; translation by Hans H. Losenthien and Siegfried H. Lehnigk, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0147716 (26 #5230)
  • [5] N. N. Krasovskiĭ, Stability of motion. Applications of Lyapunov’s second method to differential systems and equations with delay, Translated by J. L. Brenner, Stanford University Press, Stanford, Calif., 1963. MR 0147744 (26 #5258)
  • [6] J. J. Levin, On the global asymptotic behavior of nonlinear systems of differential equations, Arch. Rational Mech. Anal. 6 (1960), 65–74 (1960). MR 0119525 (22 #10286)
  • [7] 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 0119524 (22 #10285)
  • [8] A. Lyapounov, Problème général de la stabilité du mouvement, Annals of Mathematics Studies No. 17, Princeton Univ. Press, Princeton, N. J., 1949.
  • [9] J. L. Massera, On Liapounoff’s conditions of stability, Ann. of Math. (2) 50 (1949), 705–721. MR 0035354 (11,721f)
  • [10] K. P. Persidskii, Theory of stability of integrals of a system of differential equations, Izvestia, Gostehizdat, Vol. 8, 1936-1937.
  • [11] Taro Yoshizawa, On the non-linear differential equation, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 28 (1954), 133–141. MR 0065732 (16,474c)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34.51

Retrieve articles in all journals with MSC: 34.51


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1965-0178203-7
PII: S 0002-9947(1965)0178203-7
Article copyright: © Copyright 1965 American Mathematical Society