Geodesic
Finite order solutions of complex linear differential equations
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Laine, Ilpo and Yang, Ronghua},
     title = {Finite order solutions of complex linear differential equations},
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     year = {2004},
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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/