Geodesic
A differential equation without a solution
Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 125-128

Voir la notice de l'article provenant de la source Math-Net.Ru

A direct construction is given of a function $f(x_1, x_2)\in C^\infty$, such that the equation $$ \frac{\partial u}{\partial x_1}+ix_1^{2k-1}\frac{\partial u}{\partial x_2}=f $$ has no solution in any neighborhood of the origin; the function $f$ and all its derivatives vanish for $x_1=0$. 
@article{MZM_1971_10_2_a0,
     author = {V. V. Grushin},
     title = {A differential equation without a solution},
     journal = {Matemati\v{c}eskie zametki},
     pages = {125--128},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a0/}
}
TY  - JOUR
AU  - V. V. Grushin
TI  - A differential equation without a solution
JO  - Matematičeskie zametki
PY  - 1971
SP  - 125
EP  - 128
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a0/
LA  - ru
ID  - MZM_1971_10_2_a0
ER  - 
%0 Journal Article
%A V. V. Grushin
%T A differential equation without a solution
%J Matematičeskie zametki
%D 1971
%P 125-128
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a0/
%G ru
%F MZM_1971_10_2_a0
V. V. Grushin. A differential equation without a solution. Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 125-128. http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a0/