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Algebraic Schwarzian differential equations. (English) Zbl 0849.30021

Necessary conditions for the Newton polygon associated with a general differential equation algebraic in the unknown function and its Schwarzian derivative are presented in the case of existence of an admissible solution (in Nevanlinna sense). Moreover, an admissible solution is shown to satisfy a stronger version of Nevanlinna’s defect relation.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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