On a type of Volterra integral equation in the space of continuous functions with bounded variation valued in Banach spaces
Author
Leiva, Hugo
Matute, Jesús
Merentes, Nelson
Sánchez, José
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/117610.4067/S0719-06462015000200004
Abstract
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.