Representation of Solutions of a Certain Integro-Differential Equation and Applications

In this paper, we consider a second-order integro-differential equation with unbounded operator coefficients in Hilbert space, which is an abstract hyperbolic perturbed by integral term difference-type kernel of special form. This arises the description various viscoelastic systems. Using system generalized eigenvectors sheaf associated considered, construct p-basis orthogonal sum spaces. basis, find representation solution equation. We also discuss possible applications to problems viscoelasticity.