On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces

In this paper we prove existence and uniqueness of the solutions for a kind of Volterra equation, with an initial condition, in the space of the continuous functions with bounded variation which take values in an arbitrary Banach space. Then we give a parameters variation formula for the solutions o...

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Autores principales:	Leiva,Hugo, Matute,Jesús, Merentes,Nelson, Sánchez,José
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2015
Materias:	Existence and uniqueness of solutions of integral equations in Banach spaces continuous functions bounded variation norm parameters variation formula controllability
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000200004
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spelling	oai:scielo:S0719-064620150002000042018-10-08On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach SpacesLeiva,HugoMatute,JesúsMerentes,NelsonSánchez,José Existence and uniqueness of solutions of integral equations in Banach spaces continuous functions bounded variation norm parameters variation formula controllability In this paper we prove existence and uniqueness of the solutions for a kind of Volterra equation, with an initial condition, in the space of the continuous functions with bounded variation which take values in an arbitrary Banach space. Then we give a parameters variation formula for the solutions of certain kind of linear integral equation. Finally, we prove exact controllability of a particular integral equation using that formula. Moreover, under certain condition, we find a formula for a control steering of a type of system which is studied in the current work, from an initial state to a final one in a prescribed time.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.17 n.2 20152015-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000200004en10.4067/S0719-06462015000200004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Existence and uniqueness of solutions of integral equations in Banach spaces continuous functions bounded variation norm parameters variation formula controllability
spellingShingle	Existence and uniqueness of solutions of integral equations in Banach spaces continuous functions bounded variation norm parameters variation formula controllability Leiva,Hugo Matute,Jesús Merentes,Nelson Sánchez,José On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
description	In this paper we prove existence and uniqueness of the solutions for a kind of Volterra equation, with an initial condition, in the space of the continuous functions with bounded variation which take values in an arbitrary Banach space. Then we give a parameters variation formula for the solutions of certain kind of linear integral equation. Finally, we prove exact controllability of a particular integral equation using that formula. Moreover, under certain condition, we find a formula for a control steering of a type of system which is studied in the current work, from an initial state to a final one in a prescribed time.
author	Leiva,Hugo Matute,Jesús Merentes,Nelson Sánchez,José
author_facet	Leiva,Hugo Matute,Jesús Merentes,Nelson Sánchez,José
author_sort	Leiva,Hugo
title	On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
title_short	On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
title_full	On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
title_fullStr	On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
title_full_unstemmed	On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces
title_sort	on a type of volterra integral equation in the space of continuous functions with bounded variation valued in banach spaces
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2015
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000200004
work_keys_str_mv	AT leivahugo onatypeofvolterraintegralequationinthespaceofcontinuousfunctionswithboundedvariationvaluedinbanachspaces AT matutejesus onatypeofvolterraintegralequationinthespaceofcontinuousfunctionswithboundedvariationvaluedinbanachspaces AT merentesnelson onatypeofvolterraintegralequationinthespaceofcontinuousfunctionswithboundedvariationvaluedinbanachspaces AT sanchezjose onatypeofvolterraintegralequationinthespaceofcontinuousfunctionswithboundedvariationvaluedinbanachspaces
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On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces

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