Solvability and controllability of second-order non-autonomous impulsive neutral evolution hemivariational inequalities

The primary aim of this article was to explore the approximate controllability of second- order impulsive hemivariational inequalities with initial conditions in Hilbert space. The mild solution was initially derived using the properties of the cosine and sine family of operators, Clarke's subdifferential, and the fact that the related linear equation has an evolution operator. The results of the approximate controllability of the considered systems were then taken into account using the fixed-point theorem method. An application was provided to support our theoretical findings.