Geodesic
Asymptotic behavior of solutions of delay equations in Hilbert spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 77-86

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We establish unimprovable estimates of solutions of inhomogeneous delay differential-difference equations, the coefficients of which are unbounded operators and operator-functions acting in a Hilbert space. We also present results about expansions of those solutions into a sum of a (finite) linear combination of exponential solutions for the homogeneous equation and a function with a smaller power of the exponential growth. 
@article{CMFD_2007_21_a3,
     author = {D. A. Medvedev},
     title = {Asymptotic behavior of solutions of delay equations in {Hilbert} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {77--86},
     publisher = {mathdoc},
     volume = {21},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_21_a3/}
}
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D. A. Medvedev. Asymptotic behavior of solutions of delay equations in Hilbert spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 77-86. http://geodesic.mathdoc.fr/item/CMFD_2007_21_a3/