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- Scopus: eid_2-s2.0-85055689796
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Article: Nonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture
Title | Nonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture |
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Authors | |
Issue Date | 2018 |
Publisher | Magnes Press. The Journal's web site is located at http://www.springer.com/math/journal/11856 |
Citation | Israel Journal of Mathematics, 2018, v. 229 n. 1, p. 1-38 How to Cite? |
Abstract | In this paper, we consider the growth, in terms of the Nevanlinna characteristic function, of meromorphic solutions of factorizable $n$-th order algebraic ordinary differential equations. It is shown that for generic cases all their meromorphic solutions are elliptic functions or their degenerations. Moreover, for the second order factorizable algebraic ODEs, all the meromorphic solutions of them (except for one case) are found explicitly. Hence, a conjecture proposed by Hayman in 1996 is verified for these second order ODEs. |
Persistent Identifier | http://hdl.handle.net/10722/264181 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.943 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, TW | - |
dc.contributor.author | Wu, C | - |
dc.date.accessioned | 2018-10-22T07:50:50Z | - |
dc.date.available | 2018-10-22T07:50:50Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Israel Journal of Mathematics, 2018, v. 229 n. 1, p. 1-38 | - |
dc.identifier.issn | 0021-2172 | - |
dc.identifier.uri | http://hdl.handle.net/10722/264181 | - |
dc.description.abstract | In this paper, we consider the growth, in terms of the Nevanlinna characteristic function, of meromorphic solutions of factorizable $n$-th order algebraic ordinary differential equations. It is shown that for generic cases all their meromorphic solutions are elliptic functions or their degenerations. Moreover, for the second order factorizable algebraic ODEs, all the meromorphic solutions of them (except for one case) are found explicitly. Hence, a conjecture proposed by Hayman in 1996 is verified for these second order ODEs. | - |
dc.language | eng | - |
dc.publisher | Magnes Press. The Journal's web site is located at http://www.springer.com/math/journal/11856 | - |
dc.relation.ispartof | Israel Journal of Mathematics | - |
dc.title | Nonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture | - |
dc.type | Article | - |
dc.identifier.email | Ng, TW: ngtw@hku.hk | - |
dc.identifier.authority | Ng, TW=rp00768 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11856-018-1791-0 | - |
dc.identifier.scopus | eid_2-s2.0-85055689796 | - |
dc.identifier.hkuros | 295188 | - |
dc.identifier.volume | 229 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 38 | - |
dc.identifier.isi | WOS:000457585900001 | - |
dc.publisher.place | Israel | - |
dc.identifier.issnl | 0021-2172 | - |