Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 55, pp. 1-9.

Title: Painleve's determinateness theorem extended to proper coverings

Author: Claudi Meneghin (Isrc, Chiasso, Switzerland)

Abstract:
 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.