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.
@article{1176,
title = {On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces},
journal = {CUBO, A Mathematical Journal},
volume = {17},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/1176}
}
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. CUBO, A Mathematical Journal, Tome 17 (2015) 23 p. http://gdmltest.u-ga.fr/item/1176/