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.