Bulletin of the
Korean Mathematical Society BKMS

This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.

Keywords: impulsive conditions, nonlocal conditions, integro-differential equations, semigroup theory, cosine family, fixed point

MSC numbers: 93B05, 34A37, 34B10, 35R10