Geodesic
Finite order solutions of complex linear differential equations
Electronic journal of differential equations, Tome 2004 (2004)
We shall consider the growth of solutions of complex linear homogeneous differential equations

$ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\dots +A_1(z)f'+A_0(z)f=0 $

with entire coefficients. If one of the intermediate coefficients in exponentially dominating in a sector and $f$ is of finite order, then a derivative $f^{(j)}$ is asymptotically constant in a slightly smaller sector. We also find conditions on the coefficients to ensure that all transcendental solutions are of infinite order. This paper extends previous results due to Gundersen and to Belaidi and Hamani.
Classification : 30D35, 34M10
Keywords: linear differential equations, growth of solutions, iterated order 
@article{EJDE_2004__2004__a157,
     author = {Laine,  Ilpo and Yang,  Ronghua},
     title = {Finite order solutions of complex linear differential equations},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1063.30031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a157/}
}
TY  - JOUR
AU  - Laine,  Ilpo
AU  - Yang,  Ronghua
TI  - Finite order solutions of complex linear differential equations
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a157/
LA  - en
ID  - EJDE_2004__2004__a157
ER  - 
%0 Journal Article
%A Laine,  Ilpo
%A Yang,  Ronghua
%T Finite order solutions of complex linear differential equations
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a157/
%G en
%F EJDE_2004__2004__a157
Laine,  Ilpo; Yang,  Ronghua. Finite order solutions of complex linear differential equations. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a157/