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

2025/12/08 by Xu, Junfeng, Majumder, Sujoy, Mahato, Lata
#30D35 and 30D45 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.08001

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 \citeLYi, Lü et al. \citeLXY1 and Sauer and Schweizer \citeSS1. 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.

Citations

• GENERALIZED LOGARITHMIC DERIVATIVE ESTIMATES OF GOL'DBERG–GRINSHTEIN TYPE

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