Authors: Dragović, Vladimir 
Gontsov, Renat
Goryuchkina, Irina
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: From formal to actual Puiseux series solutions of algebraic differential equations of first order
Journal: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume: 24
Issue: 4
First page: 2201
Last page: 2213
Issue Date: 1-Jan-2023
Rank: ~M21
ISSN: 0391-173X
DOI: 10.2422/2036-2145.202111_015
Abstract: 
The existence, uniqueness and convergence of formal Puiseux series solutions of non-autonomous algebraic differential equations of first order at a nonsingular point of the equation is studied, including the case where the celebrated Painlevé theorem cannot be applied explicitly for the study of convergence. Several examples illustrating relationships to the Painlevé theorem and lesser-known results of Petrović are provided.
Publisher: Scuola Normale Superiore

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