Geodesic
Almost Continuability of Solutions of Differential Equations
Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 3-11.

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

We introduce the notion of almost continuability of the solution of the differential equation of first order $dy/dx=f(x,y)$ to the whole real axis. We give a criterion for the almost continuability of solutions for the case in which the right-hand side of the equation is a meromorphic function of one variable $y$: $f(x,y)=g(y)$. As an example, we work out the case of a rational and, in particular, an entire function $g(y)$.
Keywords: differential equation of first order, almost continuability, pole of a meromorphic function, rational function, Cauchy problem. 
@article{MZM_2009_85_1_a0,
     author = {S. A. Belyaev},
     title = {Almost {Continuability} of {Solutions} of {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a0/}
}
TY  - JOUR
AU  - S. A. Belyaev
TI  - Almost Continuability of Solutions of Differential Equations
JO  - Matematičeskie zametki
PY  - 2009
SP  - 3
EP  - 11
VL  - 85
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a0/
LA  - ru
ID  - MZM_2009_85_1_a0
ER  - 
%0 Journal Article
%A S. A. Belyaev
%T Almost Continuability of Solutions of Differential Equations
%J Matematičeskie zametki
%D 2009
%P 3-11
%V 85
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a0/
%G ru
%F MZM_2009_85_1_a0
S. A. Belyaev. Almost Continuability of Solutions of Differential Equations. Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a0/

[1] Yu. N. Bibikov, Kurs obyknovennykh differentsialnykh uravnenii, Vysshaya shkola, M., 1991