Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@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
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/