All meromorphic solutions of the autonomous Schwarzian differential equations-Reference-Cited by-同舟云学术

All meromorphic solutions of the autonomous Schwarzian differential equations

Published:2024-04-24 Issue:6 Volume:56 Page:2093-2114
ISSN:0024-6093
Container-title:Bulletin of the London Mathematical Society
language:en
Short-container-title:Bulletin of London Math Soc

Author:

Zhang Jie¹,Liao Liangwen²,Wu Chengfa³⁴^ORCID,Zhao Donghai¹

Affiliation:

1. School of Mathematics China University of Mining and Technology Xuzhou China

2. Department of Mathematics Nanjing University Nanjing China

3. Institute for Advanced Study Shenzhen University Shenzhen China

4. School of Mathematical Sciences Shenzhen University Shenzhen China

Abstract

AbstractThis paper considers a specific autonomous Schwarzian differential equation given by and presents a complete characterization of its transcendental meromorphic solutions, thus confirming a conjecture posed by Liao and Wu recently. By combining our results with those obtained in a previous paper (Math. Z. 2 (2022), 1657–1672), we are able to explicitly construct all transcendental meromorphic solutions of the autonomous Schwarzian differential equations. Additionally, we identify all nonconstant rational solutions of the autonomous Schwarzian differential equations, with the exception of one special case.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Link

https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/blms.13045

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