Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation
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 LYi, L\"u et al. LXY1 and Sauer and Schweizer 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.