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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 1000–1014 (Mi izv1544)

Exact and asymptotic solutions of systems with turning points

V. V. Kucherenko, Yu. V. Osipov

Abstract: A system of linear ordinary differential equations with analytic coefficients and small parameters on the derivative is considered. In a neighborhood of a turning point a new representation is constructed for the exact solution of the system in the form of a multiphase series. It is proved that this series converges uniformly with respect to the parameter. An expression is obtained for the Stokes constant at the maximal exponential.
Bibligraphy: 10 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 355–370

Bibliographic databases:

UDC: 517.94
MSC: Primary 34E20, 34E05, 34E15; Secondary 34A25, 34A20

Citation: V. V. Kucherenko, Yu. V. Osipov, “Exact and asymptotic solutions of systems with turning points”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 1000–1014; Math. USSR-Izv., 29:2 (1987), 355–370

Citation in format AMSBIB
\Bibitem{KucOsi86} \by V.~V.~Kucherenko, Yu.~V.~Osipov \paper Exact and asymptotic solutions of systems with turning points \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 5 \pages 1000--1014 \mathnet{http://mi.mathnet.ru/izv1544} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=873658} \zmath{https://zbmath.org/?q=an:0712.34075|0688.34039} \transl \jour Math. USSR-Izv. \yr 1987 \vol 29 \issue 2 \pages 355--370 \crossref{https://doi.org/10.1070/IM1987v029n02ABEH000973}