Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 114, pp. 117.
Growth of solutions to higherorder linear differential equations
with entire coefficients
Habib Habib, Benharrat Belaidi
Abstract:
In this article, we discuss the order and
hyperorder of the linear differential equation
where
are entire functions
and
are complex numbers
, and
are real numbers.
Under certain conditions, we prove that every solution
of the above equation is of infinite order. Then, we obtain an estimate
of the hyperorder. Finally, we give an estimate of the exponent of convergence
for distinct zeros of the functions
,
where
is an entire function
and of order
,
while the solution f of the
differential equation is of infinite order. Our results extend the previous
results due to Chen, Peng and Chen and others.
Submitted November 22, 2013. Published April 21, 2014.
Math Subject Classifications: 34M10, 30D35.
Key Words: Linear differential equation; entire solution; order of growth;
hyperorder of growth; fixed point.
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Habib Habib
Department of Mathematics
Laboratory of Pure and Applied Mathematics
University of Mostaganem (UMAB)
B. P. 227 Mostaganem, Algeria
email: habibhabib2927@yahoo.fr


Benharrat Belaïdi
Department of Mathematics
Laboratory of Pure and Applied Mathematics
University of Mostaganem (UMAB)
B. P. 227 Mostaganem, Algeria
email: belaidi@univmosta.dz

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