On the controllability of some partial functional integrodifferential equations with infinite delay in Banach spaces

Abstract

This work concerns the study of the controllability for some partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.