Electron. J. Diff. Equ., Vol. 2010(2010), No. 65, pp. 1-12.

Growth of solutions of higher-order linear differential equations

Karima Hamani

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 8, 2010.
Math Subject Classifications: 34A20, 30D35.
Key Words: Linear differential equation; entire function; hyper-order.

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Karima Hamani
Department of Mathematics
Laboratory of Pure and Applied Mathematics
University of Mostaganem, B. P. 227 Mostaganem, Algeria
email: hamanikarima@yahoo.fr

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