Approximate controllability of the non-autonomous impulsive evolution equation with state-dependent delay in Banach spaces. (February 2021) - Arora, S.; Mohan, Manil T.; Dabas, J.
Abstract: In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear evolution systems, properties of the resolvent operator and Schauder's fixed point theorem. Finally, we provide two concrete examples to validate our results. Highlights: Non-autonomous impulsive systems with state-dependent delay in Banach spaces. Sufficient conditions for approximate controllability. Extension of the work by Fu (2017) to separable reflexive Banach spaces.