Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 157, pp. 1-8.

Title: Linear differential equations with entire
       coefficients having the same order and type

Author: Nacera Berrighi (Univ. of Mostaganem, Algeria)
        Saada Hamouda   (Univ. of Mostaganem, Algeria)

Abstract:
 In this article, we study the growth of solutions to the
 differential equation
 $$
 f^{k}+(A_{k-1}(z)e^{P_{k-1}(z)}e^{\lambda z^m}
 +B_{k-1}(z))f^{k-1}+\dots 
 +(A_0(z)e^{P_0(z)}  e^{\lambda z^m}+B_0(z))f=0,
 $$
 where $\lambda \in \mathbb{C}^{\ast}$, $m\geq 2$ is an
 integer and $\max_{j=0,\dots ,k-1}\{ \deg P_j(z)\} <m$,
 $A_j,B_j$ $(j=0,\dots ,k-1)$ are entire functions of orders
 less than m.


Submitted October 20, 2011. Published November 21, 2011.
Math Subject Classifications: 34M10, 30D35.
Key Words: Linear differential equations; growth of solutions; hyper-order.