Third-order differential equations with three-point boundary conditions

In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interva...

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Autores principales:	Cabada Alberto, Dimitrov Nikolay D.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	third-order equations three-point boundary conditions green’s function degree theory 34b05 34b08 34b10 34b15 34b18 34b27 34l30 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/480a286aef9b4080b13b369d4f88d867
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id	oai:doaj.org-article:480a286aef9b4080b13b369d4f88d867
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spelling	oai:doaj.org-article:480a286aef9b4080b13b369d4f88d8672021-12-05T14:10:52ZThird-order differential equations with three-point boundary conditions2391-545510.1515/math-2021-0007https://doaj.org/article/480a286aef9b4080b13b369d4f88d8672021-02-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0007https://doaj.org/toc/2391-5455In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.Cabada AlbertoDimitrov Nikolay D.De Gruyterarticlethird-order equationsthree-point boundary conditionsgreen’s functiondegree theory34b0534b0834b1034b1534b1834b2734l30MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 11-31 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	third-order equations three-point boundary conditions green’s function degree theory 34b05 34b08 34b10 34b15 34b18 34b27 34l30 Mathematics QA1-939
spellingShingle	third-order equations three-point boundary conditions green’s function degree theory 34b05 34b08 34b10 34b15 34b18 34b27 34l30 Mathematics QA1-939 Cabada Alberto Dimitrov Nikolay D. Third-order differential equations with three-point boundary conditions
description	In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.
format	article
author	Cabada Alberto Dimitrov Nikolay D.
author_facet	Cabada Alberto Dimitrov Nikolay D.
author_sort	Cabada Alberto
title	Third-order differential equations with three-point boundary conditions
title_short	Third-order differential equations with three-point boundary conditions
title_full	Third-order differential equations with three-point boundary conditions
title_fullStr	Third-order differential equations with three-point boundary conditions
title_full_unstemmed	Third-order differential equations with three-point boundary conditions
title_sort	third-order differential equations with three-point boundary conditions
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/480a286aef9b4080b13b369d4f88d867
work_keys_str_mv	AT cabadaalberto thirdorderdifferentialequationswiththreepointboundaryconditions AT dimitrovnikolayd thirdorderdifferentialequationswiththreepointboundaryconditions
_version_	1718371643568422912

Third-order differential equations with three-point boundary conditions

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