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Article: Nonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture

TitleNonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture
Authors
Ng, TWWu, C
Issue Date2018
PublisherMagnes 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?
DOI: http://dx.doi.org/10.1007/s11856-018-1791-0
AbstractIn 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 Identifierhttp://hdl.handle.net/10722/264181
ISSN
0021-2172
2021 Impact Factor: 1.089
2020 SCImago Journal Rankings: 1.168
ISI Accession Number ID
WOS:000457585900001

 

DC FieldValueLanguage
dc.contributor.authorNg, TW-
dc.contributor.authorWu, C-
dc.date.accessioned2018-10-22T07:50:50Z-
dc.date.available2018-10-22T07:50:50Z-
dc.date.issued2018-
dc.identifier.citationIsrael Journal of Mathematics, 2018, v. 229 n. 1, p. 1-38-
dc.identifier.issn0021-2172-
dc.identifier.urihttp://hdl.handle.net/10722/264181-
dc.description.abstractIn 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.languageeng-
dc.publisherMagnes Press. The Journal's web site is located at http://www.springer.com/math/journal/11856-
dc.relation.ispartofIsrael Journal of Mathematics-
dc.titleNonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture-
dc.typeArticle-
dc.identifier.emailNg, TW: ngtw@hku.hk-
dc.identifier.authorityNg, TW=rp00768-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11856-018-1791-0-
dc.identifier.scopuseid_2-s2.0-85055689796-
dc.identifier.hkuros295188-
dc.identifier.volume229-
dc.identifier.issue1-
dc.identifier.spage1-
dc.identifier.epage38-
dc.identifier.isiWOS:000457585900001-
dc.publisher.placeIsrael-
dc.identifier.issnl0021-2172-

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