On impulsive functional differential inclusions with Hille–Yosida operators in Banach spaces

Abstract

We consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a Banach space assuming that its linear part is a non-densely defined Hille–Yosida operator. We assume that the multivalued nonlinearity of upper Carathèodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness. We apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results. The application to an optimization problem for an impulsive feedback control system is given.