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arXiv · 2512.08001

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

Junfeng Xu·Sujoy Majumder·Lata Mahato
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Abstract

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}, L\"{u} 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.

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Junfeng Xu, Sujoy Majumder, Lata Mahato. 2025-12-08. Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation. https://arxiv.org/abs/2512.08001

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