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Pure Mathematics 2024
微分差分方程亚纯解的性质
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Abstract:
本文研究了一类微分差分方程![\"\"](\"Edit_44a35e52-f4b0-4caa-b746-812918360a5e.png\")
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 ![\"\"](\"Edit_f6c226e0-d231-411f-96a3-5b02afb1e052.png\")
where n,m ∈？+, 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.
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