| 周志伟,张颖,黄志刚.一类方程组整函数解的非存在性[J].数学研究及应用,2024,44(2):213~224 |
| 一类方程组整函数解的非存在性 |
| Non-Existence of Entire Solution of a Type of System of Equations |
| 投稿时间：2023-03-29 修订日期：2023-08-13 |
| DOI：10.3770/j.issn:2095-2651.2024.02.008 |
| 中文关键词: 超越整函数 有限级 微分-差分方程组 |
| 英文关键词:transcendental entire function finite order system of differential-difference equations |
| 基金项目:国家自然科学基金 (Grant No.11971344). |
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| 摘要点击次数: 103 |
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| 中文摘要: |
| 本文证明了微分-差分方程组\begin{eqnarray}\begin{cases}{(f(z)f'(z))}^n+p_1^2(z)g^m(z+\eta)=Q_1(z) \\\nonumber{(g(z)g'(z))}^n+p_2^2(z)f^m(z+\eta)=Q_2(z)\end{cases}\end{eqnarray}不存在满足$\lambda(f)<\rho(f)$和$\lambda(g)<\rho(g)$的有限级超越整函数解$(f(z),g(z))$,其中$P_1(z), Q_1(z), P_2(z)$和$ Q_2(z)$为非零多项式. |
| 英文摘要: |
| In this paper, we will prove that the system of differential-difference equations \begin{eqnarray}\begin{cases}{(f(z)f'(z))}^n+p_1^2(z)g^m(z+\eta)=Q_1(z), \\\nonumber {(g(z)g'(z))}^n+p_2^2(z)f^m(z+\eta)=Q_2(z),\end{cases}\end{eqnarray} has no transcendental entire solution $(f(z),g(z))$ with $\rho(f,g)<\infty$ such that $\lambda(f)<\rho(f)$ and $\lambda(g)<\rho(g),$ where $P_1(z), Q_1(z), P_2(z)$ and $ Q_2(z)$ are non-vanishing polynomials. |
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