Abstract
Conditions under which there exists a change of variables that decomposes a countable system of differential equations are established for the entire real axis and a semiaxis. Similar problems are investigated for a countable system with pulse influence.
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References
A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).
Yu. A. Mitropol'skii, A. M. Samoilenko, and V. L. Kulik,Study of the Dichotomy of Linear Systems of Differential Equations by the Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).
A. M. Samoilenko and V. L. Kulik, “On the e-dichotomy and decomposability of a linear system of differential equations,”Differents. Uravn.,15, No. 4, 755–766 (1979).
A. M. Samoilenko and V. L. Kulik, “Decomposability of linearized systems of differential equations,”Ukr. Mat. Zh.,34, No. 5, 587–597 (1982).
B. F. Bylov, “On the structure of solutions to a system linear differential equations with almost periodic coefficients,”Mat. Sb.,68, No. 2, 215–229 (1965).
V. M., Millionshchikov, “Structure of fundamental matrices for systems with almost periodic coefficients,”Dokl. Akad. Nauk SSSR, Ser. Mat.,71, 238–291 (1966).
V. I. Tkachenko, “On the block diagonalization of almost periodic systems,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 6, 18–20 (1983).
R. A. Johnson and G. R. Sell, “Smoothness of spectral subbundles and reducibility of quasiperiodic linear differential systems,”J. Diff. Equat.,41, 262–288 (1981).
Kenneth J. Palmer, “Exponential dichotomy, integral separation and diagonalizability of linear systems of ordinary differential equations,”J. Diff. Equal.,55, No. 2, 184–203 (1982).
Kenneth J. Palmer, “An ordering for linear differential systems and a characterization of exponential separation in terms of reducibility,”J. Diff. Equat.,53, No. 1, 67–99 (1984).
J. Sacker and G. Sell, “A spectral theory for linear differential systems,”J. Diff. Equat.,27, No. 3, 320–358 (1978).
K. P. Persidskii, “Infinite systems of differential equations,” in:Differential Equations in Nonlinear Spaces [in Russian], Nauka, Alma-Ata (1976).
A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1424–1432, October, 1993.
This work was supported by the Ukrainian State Committee for Science and Technology.
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Samoilenko, A.M., Teplinskii, Y.V. On decomposability of countable systems of differential equations. Ukr Math J 45, 1598–1608 (1993). https://doi.org/10.1007/BF01571093
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DOI: https://doi.org/10.1007/BF01571093