Correct Solvability of Hyperbolic-Type Equations with Delay in a Hilbert Space

Correct solvability in the scale of Sobolev spaces on the half-line is established for an initial value problem for one class of functional differential equations with unbounded operator-valued coefficients in a Hilbert space. The cases of constant and variable time delays are analyzed. The principal part of the equations under study is an abstract hyperbolic equation in a Hilbert space.