Geodesic
On the differentiability with respect to the initial condition of a solution to an ordinary differential equation
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 115-129 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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M. F. Sukhinin. On the differentiability with respect to the initial condition of a solution to an ordinary differential equation. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 115-129. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a7/

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