A system of linear differential equations with small parameter as a coefficient of a part of derivatives is reduced to the canonical form and the properties of the transformation matrix are investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York (1965).
W. Wasow, Linear Turning Point Theory, Springer, New York (1985).
A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).
M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations [in Russian], Nauka, Moscow (1983).
M. Kohno, S.Ohkohchi, and T. Kohmoto, “On full uniform simplification of even order linear differential equations with a parameter,” Hiroshima Math. J., 9, 747–767 (1979).
W. Wasow, “Simplification of turning point problems for systems of linear differential equations,” Trans. Amer. Math. Soc., 106, 100–114 (1963).
A. M. Samoilenko, “On the asymptotic integration of one system of linear differential equations with small parameter as a coefficient of a part of derivatives,” Ukr. Mat. Zh., 54, No. 11, 1505–1516 (2002).
F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York (1974).
I. H. Klyuchnyk, “Asymptotic solutions of a linear system with small parameter as a coefficient of a part of derivatives,” Nelin. Kolyvannya, 13, No. 1, 30–38 (2010).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 625–642, May, 2010.
Rights and permissions
About this article
Cite this article
Klyuchnyk, I.H. Linear system of differential equations with turning point. Ukr Math J 62, 716–738 (2010). https://doi.org/10.1007/s11253-010-0383-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0383-x