TY  - JOUR
ID  - Hamani2017
LB  - Hamani2017
AU  - Hamani, Karima
AU  - Belaïdi, Benharrat
TI  - On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations
ST  - On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 6
SP  - 853
EP  - 874
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.6.853
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.6.853
AB  - In this paper, we investigate the growth of meromorphic solutions of the linear differential equation \[f^{(k)}+h_{k-1}(z)e^{P_{k-1}(z)}f^{(k-1)}+\ldots +h_{0}(z)e^{P_{0}(z)}f=0,\] where \(k\geq 2\) is an integer, \(P_{j}(z)\) (\(j=0,1,\ldots ,k-1\)) are nonconstant polynomials and \(h_{j}(z)\) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions. We also consider nonhomogeneous linear differential equations.
KW  - linear differential equation
KW  - transcendental meromorphic function
KW  - order of growth
KW  - hyper-order
SN  - 1232-9274
ER  -