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This article is cited in 13 scientific papers (total in 13 papers)
Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation
A. N. Godunov M. V. Lomonosov Moscow State University
Abstract:
We formulate a continuous function $F\colon R\times H\to H$, where $H$ is a separable Hilbert space such that the Cauchy problem
$$
x'(t)=F(t,x(t)),\quad x(t_0)=x_0
$$
has no solution in any neighborhood of the point $t_0$, no matter what $t_0\in R$ and $x_0\in H$ are considered.
Received: 13.04.1973
Citation:
A. N. Godunov, “Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation”, Mat. Zametki, 15:3 (1974), 467–477; Math. Notes, 15:3 (1974), 273–279
Linking options:
https://www.mathnet.ru/eng/mzm7368 https://www.mathnet.ru/eng/mzm/v15/i3/p467
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Abstract page: | 245 | Full-text PDF : | 143 | First page: | 1 |
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