On the differentiability with respect to the initial condition of a solution to an ordinary differential equation
M. F. Sukhinin
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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Mathematics of the USSR-Sbornik, 1979, 35:1, 115–129
MSC: Primary 34G20; Secondary 46G05, 47H15
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
\paper On the differentiability with respect to the initial condition of a~solution to an ordinary differential equation
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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