文献类型：期刊文献

英文题名：Properties of meromorphic solutions of first-order differential-difference equations

作者：Wu, Lihao[1];Chen, Baoqin[2];Li, Sheng[2]

机构：[1]Guangzhou City Univ Technol, Sch Comp Engn, Guangzhou 510800, Peoples R China;[2]Guangdong Ocean Univ, Sch Math & Comp, Zhanjiang 524088, Peoples R China

年份：2023

卷号：21

期号：1

外文期刊名：OPEN MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:001112523600001)、、Scopus(收录号：2-s2.0-85179484534)、WOS

基金：This work is supported by the National Natural Science Fund of China (No. 12101138), and the Open Foundation of the Guangdong Provincial Key Laboratory of Electronic Information Products Reliability Technology.

语种：英文

外文关键词：differential-difference equation; growth and zeros; meromorphic solution

外文摘要：For the first-order differential-difference equations of the form A(z)f (z + 1) + B(z)f '(z) + C(z)f (z) =F(z),where A(z), B(z), C(z), and F(z) are polynomials, the existence, growth, zeros, poles, and fixed points of their nonconstant meromorphic solutions are investigated. It is shown that all nonconstant meromorphic solutions are transcendental when deg B(z) < deg{A(z) + C(z)} + 1 and all transcendental solutions are of order at least 1. For the finite-order transcendental solution f(z), the relationship between rho(f) and max{lambda(f), lambda(1/f)} is discussed. Some examples for sharpness of our results are provided.