On the Controllability of Some Nonlinear Partial Functional Integrodifferential Equations with Finite Delay in Banach Spaces

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This work concerns the study of the controllability for some nonlinear partial functional integrodifferential equation with finite delay arising in the modelling of materials with memory 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 Monch fixed-point Theorem. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator. An example of applications is given for illustration.