Research articles
ScienceAsia 48 (2022): 107-114 |doi:
10.2306/scienceasia1513-1874.2022.027
Meromorphic solutions of some types of q-difference
differential equation and delay differential equation
Minfeng Chena,*, Zongsheng Gaob, Jilong Zhangb
ABSTRACT: In this paper, we investigate the existence of rational solutions and value distribution of non-rational
meromorphic solutions with the finite order of delay differential equation w(z + 1) ? w(z ? 1) + a
w
0
(z)
w(z)
= b,
where a ? C{0}, b ? C are constants. In addition, necessary conditions are obtained for q-difference differential
equation
w(qz) ? w(z/q) + a(z)
w
0
(z)
w(z)
= R(z, w(z))
to admit a non-rational meromorphic solution of zero-order, where |q| ∈ {0, 1}, a(z) is rational and R(z, w(z)) is rational in w(z) with rational coefficients in z.
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| a |
School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006 China |
| b |
LMIB & School of Mathematical Sciences, Beihang University, Beijing 100191 China |
* Corresponding author, E-mail: chenminfeng198710@126.com
Received 8 May 2021, Accepted 10 Nov 2021
|
