微分差分方程亚纯解的性质  

On the Properties of Meromorphic Solutions to Differential-Difference Equations

作　　者：牛文潇 

机构地区：[1]北京邮电大学,理学院,北京

出　　处：《理论数学》2024年第1期189-202,共14页Pure Mathematics

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。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.

关 键 词：亚纯函数 微分差分方程 值分布 非线性 

分 类 号：O17[理学—数学]