Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 52, pp. 1-16.

Title: Crossed differential systems of equations and Clunie lemma

Authors: Yingchun Gao (Nanchang Univ., Jiangxi, China)
         Kai Liu (Nanchang Univ., Jiangxi, China)
         Xiaoguang Qi (Univ. of Jinan, Shandong, China)

Abstract: 
We study properties of transcendental meromorphic solutions of 
crossed complex differential systems of equations.
For instance, we study the crossed Riccati differential system
 $$\displaylines{
f(z)^2=1-g'(z), \cr
g(z)^2=1-f'(z),
 }$$
and the crossed Weierstrass differential system
 $$\displaylines{
f(z)^3=1-g'(z)^2, \cr
g(z)^3=1-f'(z)^2.
 }$$
In addition, we establish a crossed version of Clunie lemma.

Submitted March 20, 2024. Published September 10, 2024.
Math Subject Classifications: 30D35, 34M05.
Key Words: Meromorphic solutions; Clunie lemma; Riccati equations;  crossed differential systems of equations.