Siberian Mathematical Journal

, Volume 37, Issue 2, pp 268–275 | Cite as

Existence of quadratic Lyapunov functionals for equations with unbounded operators in Hilbert space

  • D. R. Kozlov


Hilbert Space Unbounded Operator Lyapunov Functional 
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  1. 1.
    A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Gostekhteoretizdat, Moscow-Leningrad (1950).Google Scholar
  2. 2.
    Yu. L. Daletskii and M. G. Krein, Stability of Solutions to Differential Equations in Banach Space [in Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    G. R. Buis et al, “Lyapunov stability for partial differential equations. I,” NASA CR-1100 (1967).Google Scholar
  4. 4.
    R. Datko, “Extending a theorem of A. M. Lyapunov to Hilbert space,” J. Math. Anal. Appl.,32, No. 3, 610–616 (1970).Google Scholar
  5. 5.
    G. N. Mil'shtein, “Extension of Lyapunov's stability criterion to an equation with unbounded operator in Hilbert space,” in: Abstracts: Problems of Analytic Mechanics, Stability Theory, and Control [in Russian], Proceedings of the Chetaev Second Conference, Kazansk. Aviatsion. Inst., Kazan', 1976,2, pp. 242–250.Google Scholar
  6. 6.
    J. A. Walker, “On the application of Lyapunov's direct method to linear dynamic systems,” J. Math. Anal. Appl.,53, 187–220 (1976).Google Scholar
  7. 7.
    T. K. Sirazetdinov, Stability of Systems with Distributed Parameters [in Russian], Nauka, Novosibirsk (1987).Google Scholar
  8. 8.
    P. Grisvard, “Equations differentielles abstraites,” Ann. Sci. école Norm. Super. Ser. 4,2, 311–395 (1969).Google Scholar
  9. 9.
    N. Takao, “Feedback stabilization of diffusion equations by a functional observer,” J. Differential Equations,43, 257–280 (1982).Google Scholar
  10. 10.
    V. S. Belonosov, “On instability indices of unbounded operators,” Dokl. Akad. Nauk SSSR,273, No. 1, 11–14 (1983).Google Scholar
  11. 11.
    S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967).Google Scholar
  12. 12.
    N. N. Krasovskii, Certain Problems of Stability Theory of Motion [in Russian], Fizmatgiz, Moscow (1965).Google Scholar
  13. 13.
    S. G. Krein (ed.), Functional Analysis [in Russian], Nauka, Moscow (1972).Google Scholar
  14. 14.
    A. I. Miloslavskii, “On stability of some classes of evolution equations,” Sibirsk. Mat. Zh.,36, No. 5, 118–132 (1985).Google Scholar
  15. 15.
    N. D. Kopachevskii, S. G. Krein, and Kan Zui Ngo, Operator Methods in Nonlinear Hydrodynamics: Evolution and Spectral Problems [in Russian], Nauka, Moscow (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • D. R. Kozlov
    • 1
  1. 1.Irkutsk

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