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 Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 440–454 (Mi msb2585)

On the differentiability with respect to the initial condition of a solution to an ordinary differential equation

M. F. Sukhinin

Abstract: In this article a version of the theorem on differentiability of an implicit function is proved, and is then applied to establish a theorem on the differentiability with respect to the initial condition of a solution to an ordinary differential equation in a locally convex space obtained by introducing into a Banach space a locally convex topology satisfying certain conditions. An example is exhibited which cannot be studied by previously known theorems of this type.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 115–129

Bibliographic databases:

UDC: 517.9
MSC: Primary 34G20; Secondary 46G05, 47H15

Citation: M. F. Sukhinin, “On the differentiability with respect to the initial condition of a solution to an ordinary differential equation”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 440–454; Math. USSR-Sb., 35:1 (1979), 115–129

Citation in format AMSBIB
\Bibitem{Suk78} \by M.~F.~Sukhinin \paper On the differentiability with respect to the initial condition of a~solution to an ordinary differential equation \jour Mat. Sb. (N.S.) \yr 1978 \vol 106(148) \issue 3(7) \pages 440--454 \mathnet{http://mi.mathnet.ru/msb2585} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=505111} \zmath{https://zbmath.org/?q=an:0434.34046|0412.34062} \transl \jour Math. USSR-Sb. \yr 1979 \vol 35 \issue 1 \pages 115--129 \crossref{https://doi.org/10.1070/SM1979v035n01ABEH001456} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17500008}