Asymptotic behavior of a solution of an infinite system of linear differential equations. (English. Russian original) Zbl 0558.34043
Ukr. Math. J. 35, 544-550 (1983); translation from Ukr. Mat. Zh. 35, No. 5, 630-636 (1983).
Sufficient conditions for the prescribed asymptotic behavior of solutions of a certain infinite system of linear differential equations are given.
Reviewer: M.Greguš
MSC:
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 34A35 | Ordinary differential equations of infinite order |
| 34A30 | Linear ordinary differential equations and systems |
References:
| [1] | N. Levinson, ?The asymptotic behavior of a system of linear differential equations,? Amer. J. Math.,68, 1-6 (1946). · Zbl 0061.19706 · doi:10.2307/2371734 |
| [2] | I. M. Rapoport, Asymptotic Methods in the Theory of Differential Equations [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1954). |
| [3] | N. I. Shkil’, ?Reduction of systems of linear differential equations to general L-diagonal form,? Differents. Uravn.,2, No. 11, 1436-1443 (1966). · Zbl 0202.08404 |
| [4] | I. I. Starun, Dop. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 602-605 (1969). |
| [5] | V. V. Bolotin, Dynamical Stability of Elastic Systems [in Russian], Gostekhizdat, Moscow (1956). |
| [6] | E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill (1955). · Zbl 0064.33002 |
| [7] | V. Kh. Kharasakhal, ?Fundamental solutions of countable systems of differential equations,? Izv. Akad. Nauk Kaz. SSR, Ser. Mat. Mekh., No. 4, 98-108 (1960). |
| [8] | K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1974). |
| [9] | G. M. Fikhtengol’ts, Course of Differential and Integral Calculus [in Russian], Vol. 2, Fizmatgiz, Moscow (1969). |
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