Electron. J. Diff. Equ., Vol. 2014 (2014), No. 125, pp. 1-11.

Growth of meromorphic solutions of higher order linear differential equations

Lijun Wang, Huifang Liu

Abstract:
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.

Submitted January 27, 2014. Published May 14, 2014.
Math Subject Classifications: 30D35, 39B12.
Key Words: Meromorphic function; differential equations; growth; order.

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Lijun Wang
College of Mathematics and Information Science
Jiangxi Normal University, Nanchang 330022, China
email: lijunwangz@163.com
Huifang Liu
College of Mathematics and Information Science
Jiangxi Normal University, Nanchang 330022, China
email: liuhuifang73@sina.com, 925268196@qq.com

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