Ukrainian Mathematical Journal

, Volume 24, Issue 5, pp 510–516 | Cite as

Method of constructing Lyapunov's function for weakly nonautonomous linear systems of differential equations

  • O. B. Lykova
  • B. M. Bogatyrev


Differential Equation Linear System Nonautonomous Linear System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    N. A. Pustovoitov, “The construction of the Lyapunov function by the method of the small parameter,” Trudy Seminara po Matematicheskoi Fizike, Naukova Dumka, Kiev (1968).Google Scholar
  2. 2.
    A. G. Ilyukhin and M. O. Postovoitov, “Do pobudovi rozv'yazku sistemi liniinikh diferentsial'nikh rivnyan' metodom malogo parametra,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 12 (1967).Google Scholar
  3. 3.
    M. M. Krylov and M. M. Bogolyubov, Pro Deyaki Formal'ni Rozkladi Neliniinoi Mekhanika [in Ukrainian], Vid-vo YUAN, Kiev (1934).Google Scholar
  4. 4.
    V. I. Arnol'd, “Small denominators and the problem of the stability of motion in classical and celestial mechanics,” Usp. Matem. Nauk,18, No. 6 (1963).Google Scholar
  5. 5.
    Yu. A. Mitropol'skii, “The construction of the general solution of nonlinear differential equations by a method ensuring rapid convergence,” Ukrainsk. Matem. Zh.,16, No. 4 (1964).Google Scholar
  6. 6.
    Yu. A. Mitropol'skii and A. M. Samoilenko, “The problem of constructing solutions of nonlinear differential equations with quasiperiodic coefficients,” Matem. Fiz., No. 3, Naukova Dumka, Kiev (1967).Google Scholar
  7. 7.
    O. B. Lykova and B. M. Bogatyrev, “The reducibility of certain differential equations in a Banach space,” Ukrainsk. Matem. Zh.,20, No. 5 (1968).Google Scholar
  8. 8.
    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, A Method of Rapid Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
  9. 9.
    F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1967).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • O. B. Lykova
    • 1
  • B. M. Bogatyrev
    • 1
  1. 1.Ternopol'sk Institute of National EconomyInstitute of Mathematics of the Academy of Sciences of the Ukrainian SSRUkraine

Personalised recommendations