一类微分–差分方程的整函数解
The Entire Solutions of Certain Type of Nonlinear Difference Differenfial Equations
摘要: 本文应用Nevanlinna值分布理论来讨论一类非线性微分–差分方程整函数解的存在性等问题，推广、改进了几个已知结果。在本文中，我们考虑非线性微分–差分方程方程组的整解fn+L(z,f)=p1ea1z+p2ea2z，其中n≥3，L(z,f)表示f的线性微分–差分多项式，p1,p2,α1,α2是整函数，其级小于1。同时我们对Zhang等人提出的猜想给出了肯定的答案。
Abstract: In this paper, the Nevanlinna value distribution theory is applied to discuss the existence of integral function solutions for a class of nonlinear differential-difference equations, and some interesting and important conclusions are obtained, which are extended and improved. In this paper, we consider the entire solutions of non-linear difference-differential equation fn+L(z,f)=p1ea1z+p2ea2z,where L(z,f)denotes a difference-differential polynomial of f, and p1, p2, α1, α2 are entire functions with order less than 1. Meanwhile, we give an affirmative answer to the conjecture posed by Zhang et al.
文章引用：刘思瑶, 陈硕人. 一类微分–差分方程的整函数解[J]. 理论数学, 2021, 11(5): 903-908. https://doi.org/10.12677/PM.2021.115103

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