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.


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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