On a type of Volterra integral equation in the space of continuous functions with bounded variation valued in Banach spaces
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Hugo Leiva
hleiva@ula.ve
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Jesús Matute
jmatute@ula.ve
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Nelson Merentes
nmerucv@gmail.com
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José Sánchez
casanay085@hotmail.com
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DOI:
https://doi.org/10.4067/S0719-06462015000200004Abstract
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.
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