On a type of Volterra integral equation in the space of continuous functions with bounded variation valued in Banach spaces

Hugo Leiva; Jesús Matute; Nelson Merentes; José Sánchez

doi:10.4067/S0719-06462015000200004

Authors

Hugo Leiva Dpto. de Matemáticas, Universidad de Los Andes, La Hechicera. Mérida 5101. Venezuela.
Jesús Matute Dpto. de Matemáticas, Universidad de Los Andes, La Hechicera. Mérida 5101. Venezuela.
Nelson Merentes Escuela de Matemáticas, Universidad Central de Venezuela, Caracas. Venezuela.
José Sánchez Escuela de Matemáticas, Universidad Central de Venezuela, Caracas. Venezuela.

DOI:

https://doi.org/10.4067/S0719-06462015000200004

Keywords:

Existence and uniqueness of solutions of integral equations in Banach spaces, continuous functions, bounded variation norm, parameters variation formula, controllability

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.