Meromorphic solutions of certain nonlinear difference equations

Open Mathematics

Liu Huifang¹  Zheng Dan¹  Mao Zhiqiang² 

[1] College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China;School of Mathematics and Computer, Jiangxi Science and Technology Normal University, Nanchang, 330038, China;

关键词: difference equations;    meromorphic solutions;    exponential polynomials;    2020;    39b32;    30d35;   

DOI  :  10.1515/math-2020-0070

来源: DOAJ

【 摘 要 】

This paper focuses on finite-order meromorphic solutions of nonlinear difference equation fn(z)+q(z)eQ(z)Δcf(z)=p(z){f}^{n}(z)+q(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z), where p,q,Qp,q,Q are polynomials, n≥2n\ge 2 is an integer, and Δcf{\text{Δ}}_{c}f is the forward difference of f. A relationship between the growth and zero distribution of these solutions is obtained. Using this relationship, we obtain the form of these solutions of the aforementioned equation. Some examples are given to illustrate our results.

【 授权许可】

Unknown