Abstract
We solve the problem of reducibility of a countable linear system of standard difference equations with unbounded right-hand sides by the method of construction of iterations with accelerated convergence. For systems of this type with bounded right-hand sides, this problem is reduced to a finite-dimensional case.
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References
N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko,Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).
Yu. A. Mitropol'skii, A. M. Samoilenko, and D. I. Martynyuk,Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients [in Russian], Naukova Dumka, Kiev (1984);English translation: Kluwer AP, Dordrecht-Boston-London (1993).
D. I. Martynyuk and N. A. Perestyuk, “On the reducibility of linear systems of difference equations with quasiperiodic coefficients,”Vych. Prikl. Mat, Issue 23, 116–127 (1974).
I. N. Blinov, “Application of the method of arbitrarily rapid convergence to the solution of the problem of reducibility of linear systems with odd almost periodic coefficients,”Mat. Zametki,4, No. 6, 729–740 (1968).
B. F. Bylov, “On the structure of solutions of a system of linear differential equations with almost periodic coefficients,”Mat. Sb.,66, No. 2, 215–229 (1965).
A. M. Samoilenko, D. I. Martynyuk, and N. A. Perestyuk, “Reducibility of nonlinear almost periodic systems of difference equations on a torus,”Ukr. Mat. Zh.,46, No. 4, 404–410 (1994).
M. Urabe, “Existence theorems of quasiperiodic solutions to nonlinear differential systems,”Funkc. Ekvac,15, 75–100 (1972).
M. G. Filippov, “On the reducibility of systems of differential equations with almost periodic perturbations on an infinite-dimensional torus,”Dokl. Akad. Nauk Ukr.SSR, Ser.A, No. 3, 30–33 (1990).
A. M. Samoilenko, D. I. Martynyuk, and N. A. Perestyuk, “Reducibility of nonlinear almost periodic systems of differential equations on an infinite-dimensional torus,”Ukr. Mat. Zh.,46, No. 9, 1216–1223 (1994).
K. Palmer, “On the reducibility of almost periodic systems of linear differential equations,”J. Different. Equat.,36, 374–390 (1980).
A. M. Samoilenko and Yu. V. Teplinskii,On the Reducibility of Differential Systems in the Space of Bounded Number Sequences [in Russian], Preprint No. 89.44, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989).
Yu. V. Teplinskii and V. E. Luchik, “On the reducibility of pulse differential equations in the space of bounded number sequences,”Ukr. Mat. Zh.,42, No. 10, 1376–1382 (1990).
A. M. Samoilenko and Yu. V. Teplinskii, “On the reducibility of differential equations in the space of bounded number sequences,”Ukr. Mat. Zh.,41, No. 2,194–201 (1989).
A. M. Samoilenko and Yu. V. Teplinskii,Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 11, pp. 1533–1541, November, 1995.
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Samoilenko, A.M., Teplinskii, Y.V. On the reducibility of countable systems of linear difference equations. Ukr Math J 47, 1750–1759 (1995). https://doi.org/10.1007/BF01057923
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DOI: https://doi.org/10.1007/BF01057923