Literature cited
S. F. Freschenko, N. I. Shkil', and L. D. Nikolenko, Asymptotic Methods in the Theory of Differential Equations [in Russian], Naukova Dumka, Kiev (1966).
N. I. Shkil', “Asymptotic methods in the theory of linear differential equations with slowly varying coefficients,” Author's abstract of Ph. D. thesis, Kiev (1968).
G. D. Birkhoff, “On the asymptotic character of the solutions of certain linear differential equations containing a parameter,” Trans. Amer. Math. Soc.,9, 219–271 (1908).
I. S. Gradshtein, “Linear equations with variable coefficients and small parameters in the higher derivatives,” Matem. Sb.,27 (69), No. 1 (1950).
Yu. L. Rabinovich and M. M. Khapaev, “Linear equations with a small parameter in the higher derivative in a neighborhood of a regular singularity,” Dokl. Akad. Nauk SSSR,129, No, 2 (1959).
M. M. Khapaev, “Asymptotic expansions of solutions of ordinary linear differential equations with small coefficients in the higher derivatives in a neighborhood of an irregular singularity,” Dokl. Akad. Nauk SSSR,135, No. 6 (1960).
A. N. Tikhonov, “Systems of differential equations containing small parameters in the derivatives,” Matem. Sb.,31 (73), No. 3 (1952).
A. B. Vasil'eva, “Differential equations containing small parameters,” Matem. Sb.,31 (73), No. 3 (1952).
W. J. Trjitzinski, “Theory of linear differential equations containing a parameter,” Acta Math.,67, 1–50 (1936).
H. L. Turritin, “Asymptotic expansions of solutions of systems of ordinary differential equations containing a parameter,” Contributions to the theory of nonlinear oscillations, Vol. 2, Princeton (1952).
P. Noaillon, Mém. de la Soc. des Sci. de Liége,9 (1912).
S. F. Feshchenko, “Asymptotic expansion of a system of linear differential equations,” Ukrainsk. Matem. Zh.,7, No. 2 (1955).
W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Interscience Publishers, New York (1965).
Yu. L. Daletskii, “Asymptotic solution of a vector equation,” Dokl. Akad, Nauk SSSR,92, No. 5 (1953).
E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York (1955).
Yu. S. Bogdanov, “Transformation of a variable matrix to canonical form,” Dokl. Akad. Nauk BSSR,7, No. 3 (1963).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 25, No. 4, pp. 502–513, July–August, 1973.
Rights and permissions
About this article
Cite this article
Shkil, N.I., Grigorenko, V.K. Asymptotic representation of solutions of system of linear differential equations with slowly varying coefficients. Ukr Math J 25, 414–423 (1973). https://doi.org/10.1007/BF01085454
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01085454