Electron. J. Diff. Eqns., Vol. 2001(2001), No. 61, pp. 1-5.

Orders of solutions of an n-th order linear differential equation with entire coefficients

Benharrat Belaidi & Saada Hamouda

Abstract:
We study the solutions of the differential equation
$$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+\dots+A_{1}(z)f'+A_{0}(z) f=0, $$
where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.

Submitted July 23, 2001. Published September 17, 2001.
Math Subject Classifications: 30D35, 34M10, 34C10, 34C11.
Key Words: Linear differential equations, entire functions, order of growth.

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Benharrat Belaidi
Department of Mathematics
University of Mostaganem
B. P. 227 Mostaganem, Algeria
e-mail:belaidi.benharrat@caramail.com
Saada Hamouda
Department of Mathematics
University of Mostaganem
B. P. 227 Mostaganem, Algeria
e-mail: hamouda.saada@caramail.com

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