Electron. J. Diff. Equ., Vol. 2011 (2011), No. 157, pp. 1-8.

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

Nacera Berrighi, Saada Hamouda

Abstract:
In this article, we study the growth of solutions to the differential equation
$$\eqalign{ &f^{k}+(A_{k-1}(z)e^{P_{k-1}(z)}e^{\lambda z^m} +B_{k-1}(z))f^{k-1}+\dots \cr &+(A_0(z)e^{P_0(z)} e^{\lambda z^m}+B_0(z))f=0,\cr }$$
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.

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Nacera Berrighi
Laboratory of Pure and Applied Mathematics
University of Mostaganem
B.P. 227 Mostaganem, Algeria
email: n_berrighi@yahoo.fr
Saada Hamouda
Laboratory of Pure and Applied Mathematics
University of Mostaganem
B.P. 227 Mostaganem, Algeria
email: hamouda_saada@yahoo.fr

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