Advertisement

Ukrainian Mathematical Journal

, Volume 41, Issue 12, pp 1379–1384 | Cite as

Integral manifolds and a reduction principle in stability theory

  • Ya. S. Baris
  • O. B. Lykova
Article

Keywords

Stability Theory Integral Manifold Reduction Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    A. M. Lyapunov, The General Problem of Stability of Motion [in Russian], Nauka, Moscow-Leningrad (1950).Google Scholar
  2. 2.
    N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], Izd. Akad. Nauk Ukr. SSR, L'vov (1945).Google Scholar
  3. 3.
    Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).Google Scholar
  4. 4.
    O. B. Lykova, “A reduction principle in a Banach space,” Ukr. Mat. Zh.,23, No. 4, 464–471 (1971).Google Scholar
  5. 5.
    A. M. Samoilenko, “Investigation of dynamical systems by sign-constant functions,” Ukr. Mat. Zh.,24, No. 3, 374–384 (1972).Google Scholar
  6. 6.
    O. B. Lykova, “On a reduction principle for differential equations with unbounded operator coefficients,” Ukr. Mat. Zh.,27, No. 2, 240–243 (1975).Google Scholar
  7. 7.
    V. A. Pliss, “A reduction principle in the theory of stability,” Izv. Akad. Nauk SSSR, Ser. Mat.,28, 911–924 (1964).Google Scholar
  8. 8.
    V. A. Pliss, Integral Sets of Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).Google Scholar
  9. 9.
    Ya. S. Baris, “A reduction principle in the problem of conditional stability,” Mat. Fiz., Issue 26, 3–6 (1979).Google Scholar
  10. 10.
    K. G. Valeev and G. S. Finin, Construction of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  11. 11.
    K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1971).Google Scholar
  12. 12.
    O. B. Lykova, “On a theory of local integral manifolds,” Dokl. Akad. Nauk SSSR, Ser. A, No. 3, 19–28 (1980).Google Scholar
  13. 13.
    Ya. S. Baris and O. B. Lykova, “Approximate integral manifolds of systems of differential equations,” Preprint No. 79.8, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1979).Google Scholar
  14. 14.
    Ya. S. Baris and O. B. Lykova, “On approximate integral manifolds of systems of nonlinear differential equations,” Preprint No. 80.5, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1980).Google Scholar
  15. 15.
    A. S. Bakai and Yu. P. Stepanovskii, Adiabatic Invariants [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  16. 16.
    Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. I,” Ukr. Mat. Zh.,39, No. 4, 411–418 (1987).Google Scholar
  17. 17.
    Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. II,” Ukr. Mat. Zh.,40, No. 6, 709–716 (1988).Google Scholar
  18. 18.
    Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. III,” Ukr. Mat. Zh.,41, No. 3, 1033–1041 (1989).Google Scholar
  19. 19.
    I. G. Malkin, The Theory of Stability of Motion [in Russian], Nauka, Moscow (1966).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Ya. S. Baris
    • 1
  • O. B. Lykova
    • 1
  1. 1.Mathematics InstituteAcademy of Sciences of the Ukrainian SSRUSSR

Personalised recommendations