%0 Journal Article
%T 微分差分方程亚纯解的性质<br>On the Properties of Meromorphic Solutions to Differential-Difference Equations
%A 牛文潇
%J Pure Mathematics
%P 189-202
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/PM.2024.141021
%X 本文研究了一类微分差分方程<img src=\"Edit_44a35e52-f4b0-4caa-b746-812918360a5e.png\" alt=\"\" /> 的亚纯解的性质，其中正整数n ≥ m，L<sub>d</sub>(z,f)为f的微差分多项式，且次数d=deg(L<sub>d</sub>)≤n？1，b<sub>1</sub>,…,b<sub>m</sub>为非零常数，ω<sub>1</sub>,…,ω<sub>m</sub>为不同的非零常数。特别地，在某些特定条件下给出了方程亚纯解的表达式。<br />
The aim of this paper is to investigate the properties of meromorphic solutions to the differen-tial-difference equation <img src=\"Edit_f6c226e0-d231-411f-96a3-5b02afb1e052.png\" alt=\"\" /> where n,m ∈？<sup>+</sup>, n ≥ m, L<sub>d</sub>(z,f) is a differential-difference polynomial in f of degree d=deg(L<sub>d</sub>)≤n？1, b<sub>1</sub>,…,b<sub>m</sub> are nonzero constants, ω<sub>1</sub>,…,ω<sub>m</sub> are distinct nonzero constants. In particular, we give the exact form of meromorphic solutions of the above equation under certain conditions.
%K 亚纯函数，微分差分方程，值分布，非线性<br>Meromorphic Function
%K Differential-Difference Equation
%K Value Distribution
%K Nonlinear
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=79923