Painlevé Differential Equations in the Complex Plane (eBook)

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Dr. Valerii Gromak works at the Belarussian State University in Minsk, Belarussia.

Ilpo Laine is Professor at the Mathematics Department of the University of Joensuu, Finland.

Shun Shimomura is Professor at the Mathematics Department of Keio University, Yokohama, Japan.

Frontmatter 1
Contents 7
Chapter 1. Meromorphic nature of solutions 13
Chapter 2. Growth of Painlevé transcendents 40
Chapter 3. Value distribution of Painlevé transcendents 63
Chapter 4. The first Painlevé equation (P1) 86
Chapter 5. The second Painlevé equation (P2) 102
Chapter 6. The fourth Painlevé equation (P4) 129
Chapter 7. The third Painlevé equation (P3) 154
Chapter 8. The fifth Painlevé equation (P5) 186
Chapter 9. The sixth Painlevé equation (P6) 219
Chapter 10. Applications of Painlevé equations 255
Appendix A. Local existence and uniqueness of solutions of complex differential equations 275
Appendix B. Basic notations and facts in the Nevanlinna theory 282
Backmatter 291

lt;P>"Few books concentrating on topics in Painlevé equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painlevé equations without the need to refer to a large number of original papers on them [...]" Zentralblatt für Mathematik

"[...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers." Mathematical Reviews