Sharp estimates for solutions of systems with aftereffect

Vlasov, V.; Ivanov, S.

doi:10.1090/S1061-0022-09-01044-9

Sharp estimates for solutions of systems with aftereffect
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by V. V. Vlasov and S. A. Ivanov
Translated by: B. M. Bekker

St. Petersburg Math. J. 20 (2009), 193-211

DOI: https://doi.org/10.1090/S1061-0022-09-01044-9

Published electronically: January 30, 2009

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Abstract:

Sharp estimates are established for strong solutions of systems of differential-difference equations of both neutral and retarded type.

The approach is based on the study of the resolvent corresponding to the generator of the semigroup of shifts along the trajectories of a dynamical system. In the case of neutral type equations, the Riesz basis property of the subsystem of exponential solutions is used.

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