Yingchun Gao, Kai Liu, Xiaoguang Qi
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.
DOI: 10.58997/ejde.2024.52
Show me the PDF file (383 KB), TEX file for this article.
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Yingchun Gao Department of Mathematics Nanchang University Nanchang, Jiangxi, 330031, China email: gaoyingchun97@163.com |
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Kai Liu Department of Mathematics Nanchang University Nanchang, Jiangxi, 330031, China email: liukai418@126.com, liukai@ncu.edu.cn |
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Xiaoguang Qi School of Mathematics University of Jinan Jinan, Shandong, 250022, China email: xiaoguang.202@163.com, xiaogqi@mail.sdu.edu.cn |
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