On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911809474134016 |
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| author | Dahmani, Abdelkader Belaïdi, Benharrat |
| author_facet | Dahmani, Abdelkader Belaïdi, Benharrat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15211 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$ Dahmani, Abdelkader Belaïdi, Benharrat Complex Variables 34M10, 30D35 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. |
| title | On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$ |
| topic | Complex Variables 34M10, 30D35 |
| url | https://arxiv.org/abs/2403.15211 |