Literature cited
A. M. Lyapunov, The General Problem of Stability of Motion [in Russian], Nauka, Moscow-Leningrad (1950).
N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], Izd. Akad. Nauk Ukr. SSR, L'vov (1945).
Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).
O. B. Lykova, “A reduction principle in a Banach space,” Ukr. Mat. Zh.,23, No. 4, 464–471 (1971).
A. M. Samoilenko, “Investigation of dynamical systems by sign-constant functions,” Ukr. Mat. Zh.,24, No. 3, 374–384 (1972).
O. B. Lykova, “On a reduction principle for differential equations with unbounded operator coefficients,” Ukr. Mat. Zh.,27, No. 2, 240–243 (1975).
V. A. Pliss, “A reduction principle in the theory of stability,” Izv. Akad. Nauk SSSR, Ser. Mat.,28, 911–924 (1964).
V. A. Pliss, Integral Sets of Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).
Ya. S. Baris, “A reduction principle in the problem of conditional stability,” Mat. Fiz., Issue 26, 3–6 (1979).
K. G. Valeev and G. S. Finin, Construction of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1981).
K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1971).
O. B. Lykova, “On a theory of local integral manifolds,” Dokl. Akad. Nauk SSSR, Ser. A, No. 3, 19–28 (1980).
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).
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).
A. S. Bakai and Yu. P. Stepanovskii, Adiabatic Invariants [in Russian], Naukova Dumka, Kiev (1981).
Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. I,” Ukr. Mat. Zh.,39, No. 4, 411–418 (1987).
Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. II,” Ukr. Mat. Zh.,40, No. 6, 709–716 (1988).
Ya. S. Baris and O. B. Lykova, “On asymptotic expansions of invariant manifolds. III,” Ukr. Mat. Zh.,41, No. 3, 1033–1041 (1989).
I. G. Malkin, The Theory of Stability of Motion [in Russian], Nauka, Moscow (1966).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1607–1613, December, 1989.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056103