Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.