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**Value distribution of meromorphic solutions and their derivatives of complex differential equations.**
*(English)*
Zbl 1291.34148

Summary: We deal with the relationship between the small functions and the derivatives of solutions of higher-order linear differential equations
\[
f^{(k)}+A_{k-1}f^{(k-1)}+\cdots +A_0 f = 0,\quad k\geq 2,
\]
where \(A_j(z)(j=0,1,\dots,k-1)\) are meromorphic functions. The theorems of this paper improve the previous results given by El Farissi, Belaïdi, Wang, Lu, Liu, and Zhang.

### MSC:

34M05 | Entire and meromorphic solutions to ordinary differential equations in the complex domain |

34M03 | Linear ordinary differential equations and systems in the complex domain |

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

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\textit{A. El Farissi}, ISRN Math. Anal. 2013, Article ID 497921, 5 p. (2013; Zbl 1291.34148)

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### References:

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[10] | H. Y. Xu, J. Tu, and X. M. Zheng, “On the hyper exponent of convergence of zeros of f(j)-\varphi of higher order linear differential equations,” Advances in Difference Equations, vol. 2012, article 114, 16 pages, 2012. · Zbl 1350.34069 · doi:10.1186/1687-1847-2012-114 |

[11] | B. Belaïdi, “Some precise estimates of the hyper order of solutions of some complex linear differential equations,” Journal of Inequalities in Pure and Applied Mathematics, vol. 8, no. 4, article 107, 14 pages, 2007. · Zbl 1140.34445 |

[12] | J. Tu and T. Long, “Oscillation of complex high order linear differential equations with coefficients of finite iterated order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 66, pp. 1-13, 2009. · Zbl 1188.30043 |

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