Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations

The aim of this paper is to obtain different criteria which allow us to affirm that the one parameter family of $n^{\mathrm{th}}-$order linear differential equations, given by the following expression \[ T_n[M]\,u(t) \equiv u^{(n)}(t)+a_1(t)\, u^{(n-1)}(t)+\cdots +a_{n-1}(t)\, u'(t)+(a_{n}(t)+M...

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Detalles Bibliográficos
Autores: Cabada Fernández, Alberto, Saavedra López, Lorena
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/45452
Acceso en línea:https://hdl.handle.net/10347/45452
Access Level:acceso abierto
Palabra clave:Disconjugacy
Green's functions
Spectral theory
1202 Análisis y análisis funcional
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spelling Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equationsCabada Fernández, AlbertoSaavedra López, LorenaDisconjugacyGreen's functionsSpectral theory1202 Análisis y análisis funcionalThe aim of this paper is to obtain different criteria which allow us to affirm that the one parameter family of $n^{\mathrm{th}}-$order linear differential equations, given by the following expression \[ T_n[M]\,u(t) \equiv u^{(n)}(t)+a_1(t)\, u^{(n-1)}(t)+\cdots +a_{n-1}(t)\, u'(t)+(a_{n}(t)+M)\,u(t)=0 \,,\quad t\in I\equiv[a,b]\,, \] is not disconjugate for every $M\in \mathbb{R}$. Three different sufficient criteria, which ensure that such property holds, are presented. Moreover, a characterization of this property is given. To finish the paper, three examples, where the different criteria are applied, are shown.ElsevierUniversidade de Santiago de Compostela. Departamento de Análise Matemática20172017-03-0120172017-03-01journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/45452reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/454522026-06-15T12:47:27Z
dc.title.none.fl_str_mv Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
title Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
spellingShingle Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
Cabada Fernández, Alberto
Disconjugacy
Green's functions
Spectral theory
1202 Análisis y análisis funcional
title_short Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
title_full Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
title_fullStr Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
title_full_unstemmed Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
title_sort Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
dc.creator.none.fl_str_mv Cabada Fernández, Alberto
Saavedra López, Lorena
author Cabada Fernández, Alberto
author_facet Cabada Fernández, Alberto
Saavedra López, Lorena
author_role author
author2 Saavedra López, Lorena
author2_role author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Análise Matemática
dc.subject.none.fl_str_mv Disconjugacy
Green's functions
Spectral theory
1202 Análisis y análisis funcional
topic Disconjugacy
Green's functions
Spectral theory
1202 Análisis y análisis funcional
description The aim of this paper is to obtain different criteria which allow us to affirm that the one parameter family of $n^{\mathrm{th}}-$order linear differential equations, given by the following expression \[ T_n[M]\,u(t) \equiv u^{(n)}(t)+a_1(t)\, u^{(n-1)}(t)+\cdots +a_{n-1}(t)\, u'(t)+(a_{n}(t)+M)\,u(t)=0 \,,\quad t\in I\equiv[a,b]\,, \] is not disconjugate for every $M\in \mathbb{R}$. Three different sufficient criteria, which ensure that such property holds, are presented. Moreover, a characterization of this property is given. To finish the paper, three examples, where the different criteria are applied, are shown.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-03-01
2017
2017-03-01
dc.type.none.fl_str_mv journal 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://hdl.handle.net/10347/45452
url https://hdl.handle.net/10347/45452
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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