Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 65, pp. 1-12.
Title: Growth of solutions of higher-order linear
differential equations
Author: Karima Hamani (Univ. of Mostaganem, Algeria)
Abstract:
In this article, we study the growth of
solutions of the linear differential equation
$$
f^{(k)}+(A_{k-1}(z)e^{P_{k-1}(z)}+B_{k-1}(z)) f^{(k-1)}+\dots
+(A_0(z)e^{P_0(z)}+B_0(z))f=0,
$$
where $k\geq 2$ is an integer, $P_j(z)$ are nonconstant
polynomials and $A_j(z), B_j(z)$ are entire functions,
not identically zero. We determine the hyper-order of these
solutions, under certain conditions.
Submitted February 3, 2010. Published May 08, 2010.
Math Subject Classifications: 34A20, 30D35.
Key Words: Linear differential equation; entire function;
hyper-order.