Opuscula Mathematica
Opuscula Math. 37, no. 6 (), 853-874
http://dx.doi.org/10.7494/OpMath.2017.37.6.853
Opuscula Mathematica

On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations



Abstract. 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.
Keywords: linear differential equation, transcendental meromorphic function, order of growth, hyper-order.
Mathematics Subject Classification: 34M10, 30D35.
Cite this article as:
Karima Hamani, Benharrat Belaïdi, On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations, Opuscula Math. 37, no. 6 (2017), 853-874, http://dx.doi.org/10.7494/OpMath.2017.37.6.853
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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