Qualitative Theory of Dynamical Systems

, Volume 15, Issue 1, pp 81–93 | Cite as

On Sufficient Conditions for the Existence of Solutions for First Order Equations and Fourth Degree with the Painlevé Property

  • Khaled M’hamed-Messaoud
  • Arezki Kessi
  • Toufik Laadj


In this paper we consider the non linear Fuchs differential equation of order one and fourth degree with polynomial coefficients for the unknown and analytic in the variable. We give the sufficient conditions for Painlevé property and we list some Fuchs differential equations with fixed critical points.


Differential equations Painlevé property Fuchs theorem  Critical points 

Mathematics Subject Classification

34M55 34A34 34E20 33E30 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Khaled M’hamed-Messaoud
    • 1
  • Arezki Kessi
    • 1
  • Toufik Laadj
    • 1
  1. 1.Department of MathematicsUniversity of Science and Technology (USTHB)AlgiersAlgeria

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