References
[H] H. Herold,Differentialgleichungen im Komplexen, Vandenhoeck & Ruprecht, Göttingen, 1975.
[HL] A. Hinkkanen and I. Laine,Solutions of the first and second Painlevé equations are meromorphic, J. Analyse Math.79 (1999), 345–377.
[P] P. Painlevé,Mémoire sur les équations différentilles dont l’intégrale générale est uniforme, Bull. Soc. Math. France28 (1900), 201–261.
[St] N. Steinmetz,On Painlevé’s equations I, II and IV, J. Analyse Math.82 (2000), 363–377.
[W] W. Walter,Differential and Integral Inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
Author information
Authors and Affiliations
Additional information
This research was performed while the first author was visiting the University of Joensuu and the Mekrijärvi Research Station of the University of Joensuu. The authors would like to thank the Väisälä Fund of the Finnish Academy of Sciences and Letters for funding. The research of the second author has also been supported in part by the U.S. National Science Foundation grant DMS-9970281.
Rights and permissions
About this article
Cite this article
Hinkkanen, A., Laine, I. Solutions of a modified third Painlevé equation are meromorphic. J. Anal. Math. 85, 323–337 (2001). https://doi.org/10.1007/BF02788086
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02788086