Order and hyper-order of entire solutions of linear differential equations with entire coefficients
Date
2003-02-20
Authors
Belaidi, Benharrat
Hamani, Karima
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper, we investigate the growth of solutions of the differential equation
ƒ(k) + Ak-1 (z)ƒ(k-1) + ··· + A1(z)ƒ' + A0(z)ƒ = 0,
where A0(z),..., Ak-1(z) are entire functions with A0(z) ≢ 0. We will show that if the coefficients satisfy certain growth conditions, then every finite order solution of the equation will satisfy certain other growth conditions. We will also find conditions on the coefficients so that every solution f ≢ 0 will have infinite order and we estimate in one case that lower bounds of the hyper-order.
Description
Keywords
Linear differential equations, Growth of entire functions, Hyper-order
Citation
Belaidi, B., & Hamani, K. (2003). Order and hyper-order of entire solutions of linear differential equations with entire coefficients. <i>Electronic Journal of Differential Equations, 2003</i>(17), pp. 1-12.
Rights
Attribution 4.0 International