On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n

In this paper we deal with differential equations of the form yy' = P(x, y) where y' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for...

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Detalles Bibliográficos
Autores: Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221356
Acceso en línea:https://ddd.uab.cat/record/221356
https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6
Access Level:acceso abierto
Palabra clave:Polynomial differential equation
Polynomial solution
Linear differential equation
Riccati differential equation
Abel differential equation
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spelling On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y nFerragut Amengual, Antoni Manel|||0000-0002-7420-5004Llibre, Jaume|||0000-0002-9511-5999Polynomial differential equationPolynomial solutionLinear differential equationRiccati differential equationAbel differential equationIn this paper we deal with differential equations of the form yy' = P(x, y) where y' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/221356https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PEuropean Commission https://doi.org/10.13039/501100000780 318999open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2213562026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
title On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
spellingShingle On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004
Polynomial differential equation
Polynomial solution
Linear differential equation
Riccati differential equation
Abel differential equation
title_short On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
title_full On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
title_fullStr On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
title_full_unstemmed On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
title_sort On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
dc.creator.none.fl_str_mv Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004
Llibre, Jaume|||0000-0002-9511-5999
author Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004
author_facet Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Polynomial differential equation
Polynomial solution
Linear differential equation
Riccati differential equation
Abel differential equation
topic Polynomial differential equation
Polynomial solution
Linear differential equation
Riccati differential equation
Abel differential equation
description In this paper we deal with differential equations of the form yy' = P(x, y) where y' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/221356
https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6
url https://ddd.uab.cat/record/221356
https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
European Commission https://doi.org/10.13039/501100000780 318999
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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