Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 65, pp. 1-8.

Title: Finite order solutions of complex linear differential equations

Authors: Ilpo Laine (Univ. of Joensuu, Finland)
   Ronghua Yang (Univ. of Joensuu, Finland)

Abstract:
 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.

Submitted December 10, 2003. Published April 28, 2004.
Math Subject Classifications: 30D35, 34M10.
Key Words: Linear differential equations; growth of solutions; iterated order.