Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918239068487680 |
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| author | Xu, Junfeng Majumder, Sujoy Mahato, Lata |
| author_facet | Xu, Junfeng Majumder, Sujoy Mahato, Lata |
| contents | In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, Lü et al. \cite{LXY1} and Sauer and Schweizer \cite{SS1}. Furthermore, we show that our results reveal a deep relationship between the value-sharing behavior of an entire function $f$ and its $k$-th derivative $f^{(k)}$, and the analytic structure of a particular type of nonlinear differential equation. Several examples are provided to illustrate the necessity of the conditions used in our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation Xu, Junfeng Majumder, Sujoy Mahato, Lata Complex Variables 30D35 and 30D45 In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, Lü et al. \cite{LXY1} and Sauer and Schweizer \cite{SS1}. Furthermore, we show that our results reveal a deep relationship between the value-sharing behavior of an entire function $f$ and its $k$-th derivative $f^{(k)}$, and the analytic structure of a particular type of nonlinear differential equation. Several examples are provided to illustrate the necessity of the conditions used in our results. |
| title | Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation |
| topic | Complex Variables 30D35 and 30D45 |
| url | https://arxiv.org/abs/2512.08001 |