Geodesic
Correct Solvability of Hyperbolic-Type Equations with Delay in a~Hilbert Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 127-137

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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. 
@article{TM_2003_243_a10,
     author = {V. V. Vlasov and K. I. Shmatov},
     title = {Correct {Solvability} of {Hyperbolic-Type} {Equations} with {Delay} in {a~Hilbert} {Space}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {127--137},
     publisher = {mathdoc},
     volume = {243},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_243_a10/}
}
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V. V. Vlasov; K. I. Shmatov. Correct Solvability of Hyperbolic-Type Equations with Delay in a~Hilbert Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 127-137. http://geodesic.mathdoc.fr/item/TM_2003_243_a10/