一类微分差分方程的整函数解

吴丽镐, 张然然, 黄志波

数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 471-478.

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数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 471-478. DOI: 10.12386/A2021sxxb0040
论文

一类微分差分方程的整函数解

    吴丽镐1, 张然然2, 黄志波3
作者信息 +

Entire Solutions to a Certain Type of Differential-difference Equations

    Li Hao WU1, Ran Ran ZHANG2, Zhi Bo HUANG3
Author information +
文章历史 +

摘要

本文考虑一类非线性微分差分方程f（z）n+L（z，f）=q（z）ep（z），其中n ≥ 2为自然数，L（z，f）（≢ 0）是关于f（z）的线性微分差分多项式，p（z）和q（z）是非零多项式.在该方程具有超级小于1的超越整函数解的假设下，证明了n=2且λ（f）=σ（f）=deg p（z），并给出二次微分差分方程整函数解的具体表示.

Abstract

We investigate the nonlinear differential-difference equations of form f(z)n+ L(z, f)=q(z)ep(z), where n ≥ 2, L(z, f)(≢ 0) is a linear differential-difference polynomial in f(z), with small functions as its coefficients, p(z) and q(z) are non-vanishing polynomials. We first obtain that n=2 and f(z) satisfies λ(f)=σ(f)=deg p(z) if the equation possesses a transcendental entire solution of hyper order σ2(f)< 1. Furthermore, the exact form of the entire solutions of the equation is also obtained.

关键词

微分差分方程 / 差分方程 / 整函数解

Key words

differential-difference equation / difference equation / entire solution

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吴丽镐, 张然然, 黄志波. 一类微分差分方程的整函数解. 数学学报, 2021, 64(3): 471-478 https://doi.org/10.12386/A2021sxxb0040
Li Hao WU, Ran Ran ZHANG, Zhi Bo HUANG. Entire Solutions to a Certain Type of Differential-difference Equations. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 471-478 https://doi.org/10.12386/A2021sxxb0040

参考文献

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基金

国家自然科学基金（11801093，11871260）；广东省自然科学基金（2018A030313508）；广东省普通高校特色创新类项目（2019KTSCX119）；广州市科技计划（202002030228）
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