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Cubo (Temuco)

On-line version ISSN 0719-0646

Abstract

LEIVA, Hugo; MATUTE, Jesús; MERENTES, Nelson  and  SANCHEZ, José. On a Type of Volterra Integral Equation in the Space of Continuous Functions with Bounded Variation valued in Banach Spaces. Cubo [online]. 2015, vol.17, n.2, pp.49-72. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462015000200004.

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.

Keywords : Existence and uniqueness of solutions of integral equations in Banach spaces; continuous functions; bounded variation norm; parameters variation formula; controllability.

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