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St. Petersburg Mathematical Journal

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Sharp estimates for solutions of systems with aftereffect


Authors: V. V. Vlasov and S. A. Ivanov
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 20 (2008), nomer 2.
Journal: St. Petersburg Math. J. 20 (2009), 193-211
MSC (2000): Primary 34K12
DOI: https://doi.org/10.1090/S1061-0022-09-01044-9
Published electronically: January 30, 2009
MathSciNet review: 2423996
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

V. V. Vlasov
Affiliation: Moscow State University, Leninskiye Gory, Moscow, 119992, Russia
Email: vlasov@math.mipt.ru, vikvvlasov@rambler.ru

S. A. Ivanov
Affiliation: St. Petersburg State University, Russian Center of Laser Physics, Ulyanovskaya 1, St. Petersburg, 198904, Russia
Email: Sergei.Ivanov@pobox.spbu.ru

DOI: https://doi.org/10.1090/S1061-0022-09-01044-9
Keywords: Differential-difference equation, retarded type, neutral type, neutral-neutral type
Received by editor(s): November 14, 2006
Published electronically: January 30, 2009
Additional Notes: Supported by RFBR (grant no. 05-01-00989) and by grant NSh-5247.2006.1
Article copyright: © Copyright 2009 American Mathematical Society

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