Controllability results in α-norm for some partial functional integrodifferential equations with infinite delay in Banach spaces

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Résumé

This work concerns the controllability in the alpha-norm for some partial functional integrodifferential equations with infinite delay in Banach spaces. We give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained using the Schauder’s
fixed-point theorem.

Mots-clés

controllability; partial functional integrodifferenttial; analytic semigroup; resolvent operator; Schauder fixed point theorem.