Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

Keywords: controllability, semi-linear neutral impulsive inclusions, convex multi-valued map, fixed point

MSC numbers: 34A37, 34G20, 34K20, 93B05, 93C10