03597nam 22007334a 450 991045462610332120200520144314.01-282-19434-897866121943443-11-019809-610.1515/9783110198096(CKB)1000000000688549(EBL)314057(OCoLC)270933131(SSID)ssj0000217517(PQKBManifestationID)11198558(PQKBTitleCode)TC0000217517(PQKBWorkID)10202855(PQKB)11314695(MiAaPQ)EBC314057(DE-B1597)32328(OCoLC)979761462(DE-B1597)9783110198096(PPN)175563764sudoc(PPN)140490396(Au-PeEL)EBL314057(CaPaEBR)ebr10194843(CaONFJC)MIL219434(OCoLC)935264337(EXLCZ)99100000000068854920020729d2002 uy 0engur|n|---|||||txtccrPainlevé differential equations in the complex plane[electronic resource] /Valerii I. Gromak, Ilpo Laine, Shun ShimomuraReprint 2013Berlin ;New York Walter de Gruyterc20021 online resource (312 p.)De Gruyter studies in mathematics ;28Description based upon print version of record.3-11-017379-4 Includes bibliographical references (p. [283]-299) and index. Frontmatter -- Contents -- Chapter 1. Meromorphic nature of solutions -- Chapter 2. Growth of Painlevé transcendents -- Chapter 3. Value distribution of Painlevé transcendents -- Chapter 4. The first Painlevé equation (P1) -- Chapter 5. The second Painlevé equation (P2) -- Chapter 6. The fourth Painlevé equation (P4) -- Chapter 7. The third Painlevé equation (P3) -- Chapter 8. The fifth Painlevé equation (P5) -- Chapter 9. The sixth Painlevé equation (P6) -- Chapter 10. Applications of Painlevé equations -- Appendix A. Local existence and uniqueness of solutions of complex differential equations -- Appendix B. Basic notations and facts in the Nevanlinna theory -- BackmatterThis book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution of Painlevé transcendents. The subsequent main part of the book is devoted to topics of classical background such as representations and expansions of solutions, solutions of special type like rational and special transcendental solutions, Bäcklund transformations and higher order analogues, treatedGruyter studies in mathematics ;28.Painlevé equationsFunctions of complex variablesElectronic books.Painlevé equations.Functions of complex variables.515/.352SK 520rvkGromak V. I(Valeriĭ Ivanovich)1053009Laine Ilpo451344Shimomura Shun1053010MiAaPQMiAaPQMiAaPQBOOK9910454626103321Painlevé differential equations in the complex plane2484635UNINA