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From formal to actual Puiseux series solutions of algebraic differential equations of first order

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. 2023. Vol. 24. No. 4. P. 2201–2213.
Dragovic V., Gontsov R., Goryuchkina I.

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 Painleve theorem cannot be applied explicitly for the study of convergence. Several examples illustrating relationships to the Painleve theorem and lesser-known results of Petrovic are provided.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: convergencePuiseux seriesalgebraic differential equationPainleve theorem
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