Gromak V.I., Laine I., Shimomura S. Painleve Differential Equations in the Complex Plane

Berlin: Walter de Gruyter, 2002. — 303 p. — ISBN: 3-11-017379-4Meromorphic nature of solutions
Growth of Painlevé transcendents
Value distribution of Painlevé transcendents
The first Painlevé equation (P1)
The second Painlevé equation (P2)
The fourth Painlevé equation (P4)
The third Painlevé equation (P3)
The fifth Painlevé equation (P5)
The sixth Painlevé equation (P6)
Applications of Painlevé equations
Appendix
Local existence and uniqueness of solutions of complex differential equations
Basic notations and facts in the Nevanlinna theory