On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$

Abdelkader Dahmani; Benharrat Belaïdi

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arXiv · 2403.15211

On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$

Abdelkader Dahmani·Benharrat Belaïdi

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Abstract

In this article, we study the growth of solutions of the homogeneous complex linear differential equation \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{\prime}+ A_{0}(z)f=0, \end{equation*}% where the coefficients $A_{j}(z)$ $(j=0,1,\ldots ,k-1)$ are analytic or meromorphic functions in $\overline{\mathbb{C}}\setminus\{z_{0}\}$. Under the sufficient condition that there exists one dominant coefficient by its logarithmic lower order or by its logarithmic lower type. We extend some precedent results due to Liu, Long and Zeng and others.

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Abdelkader Dahmani, Benharrat Belaïdi. 2024-03-22. On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$. https://arxiv.org/abs/2403.15211

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