Growth of meromorphic solutions of higher order linear differential equations. (English) Zbl 1295.30076

Summary: In this article, we investigate the growth of meromorphic solutions of the differential equations \[ \displaylines{ f^{(k)}+A_{k-1}f^{(k-1)}+\dots+A_0f=0,\cr f^{(k)}+A_{k-1}f^{(k-1)}+\dots+A_0f=F,} \] where \(A_j, f\) \((j=0,\dots,k-1)\) are meromorphic functions. When there exists one dominant coefficient with lower order less than 1/2, we obtain some estimations of the hyper order and the hyper convergence exponent of zeros of meromorphic solutions of the above equations.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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