Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 467-477
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A. N. Godunov. Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 467-477. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a13/
@article{MZM_1974_15_3_a13,
author = {A. N. Godunov},
title = {Peano's theorem in an infinite-dimensional {Hilbert} space is false even in a~weakened formulation},
journal = {Matemati\v{c}eskie zametki},
pages = {467--477},
year = {1974},
volume = {15},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a13/}
}
TY - JOUR
AU - A. N. Godunov
TI - Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation
JO - Matematičeskie zametki
PY - 1974
SP - 467
EP - 477
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a13/
LA - ru
ID - MZM_1974_15_3_a13
ER -
%0 Journal Article
%A A. N. Godunov
%T Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation
%J Matematičeskie zametki
%D 1974
%P 467-477
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a13/
%G ru
%F MZM_1974_15_3_a13
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.
