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Volume 47 Number 6 Volume 48 Number 1

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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