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On hyper-order of solutions of higher order linear differential equations with meromorphic coefficients. (English) Zbl 1419.34237

Summary: In this paper, we investigate the growth of meromorphic solutions of the differential equations \[ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0 \] and \[ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=F(z), \] where \(A_{0}(z)\not\equiv0, A_{1}(z),\dots, A_{k-1}(z)\) and \(F(z)\not \equiv 0\) are meromorphic functions. A precise estimation of the hyper-order of meromorphic solutions of the above equations is given provided that there exists one dominant coefficient, which improves and extends previous results given by Belaïdi, Chen, etc.

MSC:

34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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References:

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