In this paper, we study a complete second-order integro-differential operator equation in Hilbert space. The difference-type kernel of an integral perturbation is holomorphic semigroup bordered by unbounded operators. asymptotic behavior solutions studied. Asymptotic formulas for are proved the case when right-hand side close to almost periodic function. obtained applied problem forced longitud...

The purpose of this study is to use resolvent operators investigate the existence and controllability a mild solution second-order semilinear integro-differential problem. To construct our criterion, we fixed point theorem in conjunction with measures noncompactness. A practical example used illustrate obtained results.