Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary

In this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary: \begin{equation*} u^{\prime \prime }\left( t\right) -m^{2}u\left( t\right) +f( t,e^{-...

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Detalles Bibliográficos
Autores: Cabada Fernández, Alberto, Khaldi, Rabah
Tipo de recurso: artículo
Fecha de publicación:2021
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:10347/37954
Acceso en línea:https://hdl.handle.net/10347/37954
Access Level:acceso abierto
Palabra clave:Boundary value problems
Integral boundary conditions
Upper and lower solutions method
Existence of solution
120219 Ecuaciones diferenciales ordinarias
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spelling Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundaryCabada Fernández, AlbertoKhaldi, RabahBoundary value problemsIntegral boundary conditionsUpper and lower solutions methodExistence of solution120219 Ecuaciones diferenciales ordinariasIn this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary: \begin{equation*} u^{\prime \prime }\left( t\right) -m^{2}u\left( t\right) +f( t,e^{-mt}u\left( t\right) ,e^{-mt}\,u^{\prime }\left( t\right)) =0,\quad \mbox{for all}\;t\in % \left[ 0,+\infty \right) , \label{1.1} \end{equation*} \begin{equation*} \label{1.2} u\left( 0\right) -\frac{1}{m}u^{\prime }\left( 0\right) =\int\limits_{0}^{+\infty }e^{-2ms}u\left( s\right) ds,\underset{% t\rightarrow +\infty }{\lim }{\left\{e^{-mt}u\left( t\right) \right\}} =B, \end{equation*}% where $m>0,m\neq \frac{1}{6},B\in \mathbb{R}$ and $f:\left[ 0,+\infty \right) \times \mathbb{R}^{2}\rightarrow \mathbb{R} $ is a continuous function satisfying a suitable locally $L^1$ bounded condition and a kind of Nagumo's condition with respect to the first derivative.Malaya Journal of MatematikUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización20212021-06-0420212021-06-04journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/37954reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Copyright (c) 2021 Alberto Cabada, Rabah Khaldihttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/379542026-06-15T12:47:27Z
dc.title.none.fl_str_mv Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
title Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
spellingShingle Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
Cabada Fernández, Alberto
Boundary value problems
Integral boundary conditions
Upper and lower solutions method
Existence of solution
120219 Ecuaciones diferenciales ordinarias
title_short Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
title_full Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
title_fullStr Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
title_full_unstemmed Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
title_sort Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
dc.creator.none.fl_str_mv Cabada Fernández, Alberto
Khaldi, Rabah
author Cabada Fernández, Alberto
author_facet Cabada Fernández, Alberto
Khaldi, Rabah
author_role author
author2 Khaldi, Rabah
author2_role author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
dc.subject.none.fl_str_mv Boundary value problems
Integral boundary conditions
Upper and lower solutions method
Existence of solution
120219 Ecuaciones diferenciales ordinarias
topic Boundary value problems
Integral boundary conditions
Upper and lower solutions method
Existence of solution
120219 Ecuaciones diferenciales ordinarias
description In this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary: \begin{equation*} u^{\prime \prime }\left( t\right) -m^{2}u\left( t\right) +f( t,e^{-mt}u\left( t\right) ,e^{-mt}\,u^{\prime }\left( t\right)) =0,\quad \mbox{for all}\;t\in % \left[ 0,+\infty \right) , \label{1.1} \end{equation*} \begin{equation*} \label{1.2} u\left( 0\right) -\frac{1}{m}u^{\prime }\left( 0\right) =\int\limits_{0}^{+\infty }e^{-2ms}u\left( s\right) ds,\underset{% t\rightarrow +\infty }{\lim }{\left\{e^{-mt}u\left( t\right) \right\}} =B, \end{equation*}% where $m>0,m\neq \frac{1}{6},B\in \mathbb{R}$ and $f:\left[ 0,+\infty \right) \times \mathbb{R}^{2}\rightarrow \mathbb{R} $ is a continuous function satisfying a suitable locally $L^1$ bounded condition and a kind of Nagumo's condition with respect to the first derivative.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-06-04
2021
2021-06-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/37954
url https://hdl.handle.net/10347/37954
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
Copyright (c) 2021 Alberto Cabada, Rabah Khaldi
http://creativecommons.org/licenses/by/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
Copyright (c) 2021 Alberto Cabada, Rabah Khaldi
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Malaya Journal of Matematik
publisher.none.fl_str_mv Malaya Journal of Matematik
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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score 15,812429

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