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All meromorphic solutions of the autonomous Schwarzian differential equations.
- Source :
-
Bulletin of the London Mathematical Society . Jun2024, Vol. 56 Issue 6, p2093-2114. 22p. - Publication Year :
- 2024
-
Abstract
- This paper considers a specific autonomous Schwarzian differential equation given by Sf=c(f−σ1)(f−σ2)/[(f−τ1)(f−τ2)]$$\begin{equation*} \hspace*{35pt} S_f=c(f-\sigma _1)(f-\sigma _2)/[(f-\tau _1)(f-\tau _2)] \end{equation*}$$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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTONOMOUS differential equations
*MATHEMATICS
*LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 00246093
- Volume :
- 56
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Bulletin of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 177677117
- Full Text :
- https://doi.org/10.1112/blms.13045