Ukrainian Mathematical Journal

, Volume 28, Issue 3, pp 273–283 | Cite as

Quasi-periodic solutions of differential-functional equations

  • V. I. Fodchuk
  • M. S. Bortei


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Literature cited

  1. 1.
    N. M. Krylov and N. N. Bogolyubov, Application of the Methods of Nonlinear Mechanics to the Theory of Stationary Oscillations [in Russian], Izd. Akad. Nauk UkrSSR (1934).Google Scholar
  2. 2.
    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
  3. 3.
    A. N. Kolmogorov, “General theory of dynamic systems and classical mechanics,” International Mathematical Congress in Amsterdam [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  4. 4.
    V. I. Arnol'd, “Small denominators, II. Proof of Kolmogorov's theorem on the invariance of quasiperiodic motions under small perturbations of the Hamiltonian,” Usp. Matem. Nauk,18, No. 5 (1963).Google Scholar
  5. 5.
    N. N. Bogolyubov, “On quasi-periodic solutions in nonlinear mechanics,” in: First Mathematics Summer School [in Russian], Part 1, Naukova Dumka, Kiev (1964).Google Scholar
  6. 6.
    Yu. A. Mitropol'skii, “Construction of the general solution of nonlinear differential equations by a method guaranteeing ‘accelerated convergence,’” Ukrainsk. Matem. Zh.,16, No. 4 (1964).Google Scholar
  7. 7.
    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, The Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
  8. 8.
    V. I. Fodchuk, “Integral manifolds for nonlinear differential equations with delayed argument,” Ukrainsk. Matem. Zh.,21, No. 5 (1969).Google Scholar
  9. 9.
    V. I. Fodchuk, “Integral manifolds for nonlinear differential equations with delayed argument,” Differents. Uravnen.,6, No. 5 (1970).Google Scholar
  10. 10.
    V. I. Fodchuk, “On invariant manifolds for systems with a delay,” All-Union Conference on the Qualitative Theory of Differential Equations (Abstracts of Reports) [in Russian], Sverdlovsk (1971).Google Scholar
  11. 11.
    S. N. Shimanov, “On the theory of linear differential equations with an aftereffect,” Differents, Uravnen.,1, No. 1 (1965).Google Scholar
  12. 12.
    J. K. Hale, “Linear functional-differential equations with constant coefficients,” Contrib, Diff. Equat.,2 (1963).Google Scholar
  13. 13.
    E. Hille and R. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ., Vol. 31 (1957).Google Scholar
  14. 14.
    M. M. Vainberg, Variational Methods of Investigating Nonlinear Operators [in Russian], GITTL, Moscow (1956).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • V. I. Fodchuk
    • 1
  • M. S. Bortei
    • 1
  1. 1.Chernovtsy State UniversityUSSR

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