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On the hammerstein-volterra equation in the space of the absolutely continuous functions

Abstract:

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, this formula of variation of parameters is used to study the controllability of the equations which were mentioned.