Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation

Fuente: arXiv
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Autores principales: Xu, Junfeng, Majumder, Sujoy, Mahato, Lata
Formato: Preprint
Publicado: 2025
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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