微分差分方程亚纯解的性质
On the Properties of Meromorphic Solutions to Differential-Difference Equations
DOI: 10.12677/PM.2024.141021, PDF,    国家自然科学基金支持
作者: 牛文潇：北京邮电大学，理学院，北京
关键词: 亚纯函数；微分差分方程；值分布；非线性；Meromorphic Function； Differential-Difference Equation； Value Distribution； Nonlinear
摘要: 本文研究了一类微分差分方程 的亚纯解的性质，其中正整数n ≥ m，Ld(z,f)为f的微差分多项式，且次数d=deg(Ld)≤n−1，b1,…,bm为非零常数，ω1,…,ωm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。
Abstract: The aim of this paper is to investigate the properties of meromorphic solutions to the differen-tial-difference equation where n,m ∈ℕ+, n ≥ m, Ld(z,f) is a differential-difference polynomial in f of degree d=deg(Ld)≤n−1, b1,…,bm are nonzero constants, ω1,…,ωm are distinct nonzero constants. In particular, we give the exact form of meromorphic solutions of the above equation under certain conditions.
文章引用：牛文潇. 微分差分方程亚纯解的性质[J]. 理论数学, 2024, 14(1): 189-202. https://doi.org/10.12677/PM.2024.141021

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