Electron. J. Diff. Equ., Vol. 2010(2010), No. 55, pp. 1-9.

Painleve's determinateness theorem extended to proper coverings

Claudi Meneghin

We extend Painleve's determinateness theorem to first-order ordinary differential equations in the complex domain, with known terms allowed be multivalued in the dependent variable. The multivaluedness is supposed to be resolved by proper coverings.

Submitted January 23, 2009. Published April 19, 2010.
Math Subject Classifications: 34M35, 34M45.
Key Words: Painleve's determinateness theorem; complex differential equations; Cauchy's problem; analytic continuation; singularities; multi-valued function; Riemann surface.

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Claudi Meneghin
(Isrc) - Fermo Posta Chiasso 1
CH-6830 Chiasso, Switzerland
email: claudi.meneghin@gmail.com

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