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Integral manifolds and a reduction principle in stability theory

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Literature cited

  1. A. M. Lyapunov, The General Problem of Stability of Motion [in Russian], Nauka, Moscow-Leningrad (1950).

    Google Scholar 

  2. N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], Izd. Akad. Nauk Ukr. SSR, L'vov (1945).

    Google Scholar 

  3. Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  4. O. B. Lykova, “A reduction principle in a Banach space,” Ukr. Mat. Zh.,23, No. 4, 464–471 (1971).

    Google Scholar 

  5. A. M. Samoilenko, “Investigation of dynamical systems by sign-constant functions,” Ukr. Mat. Zh.,24, No. 3, 374–384 (1972).

    Google Scholar 

  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. V. A. Pliss, “A reduction principle in the theory of stability,” Izv. Akad. Nauk SSSR, Ser. Mat.,28, 911–924 (1964).

    Google Scholar 

  8. V. A. Pliss, Integral Sets of Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  9. Ya. S. Baris, “A reduction principle in the problem of conditional stability,” Mat. Fiz., Issue 26, 3–6 (1979).

  10. K. G. Valeev and G. S. Finin, Construction of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  11. K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1971).

    Google Scholar 

  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. 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. 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. A. S. Bakai and Yu. P. Stepanovskii, Adiabatic Invariants [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  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. 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. 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. I. G. Malkin, The Theory of Stability of Motion [in Russian], Nauka, Moscow (1966).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1607–1613, December, 1989.

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Baris, Y.S., Lykova, O.B. Integral manifolds and a reduction principle in stability theory. Ukr Math J 41, 1379–1384 (1989). https://doi.org/10.1007/BF01056103

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