Finite order solutions of complex linear differential equations
Date
2004-04-28
Authors
Laine, Ilpo
Yang, Ronghua
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We shall consider the growth of solutions of complex linear homogeneous differential equations
ƒ(k) + Ak-1(z) ƒ(k-1) +‧‧‧+ A1(z) ƒ' + A0(z) ƒ = 0
with entire coefficients. If one of the intermediate coefficients in exponentially dominating in a sector and ƒ is of finite order, then a derivative ƒ(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 Belaïdi and Hamani.
Description
Keywords
Linear differential equations, Growth of solutions, Iterated order
Citation
Laine, I., & Yang, R. (2004). Finite order solutions of complex linear differential equations. <i>Electronic Journal of Differential Equations, 2004</i>(65), pp. 1-8.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.