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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 6, Pages 1413–1432 (Mi smj2393)

Behavior at infinity of a solution to a differential-difference equation

M. S. Sgibnev

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We obtain an asymptotic expansion for a solution to an $m$th order nonhomogeneous differential-difference equation of retarded or neutral type. Account is taken of the influence of the roots of the characteristic equation. The exact asymptotics of the remainder is established depending on the asymptotic properties of the free term of the equation.

Keywords: differential-difference equations, retarded-type equation, neutral-type equation, asymptotic behavior, characteristic equation.

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English version:
Siberian Mathematical Journal, 2012, 53:6, 1139–1154

Bibliographic databases:

UDC: 517.929.8

Citation: M. S. Sgibnev, “Behavior at infinity of a solution to a differential-difference equation”, Sibirsk. Mat. Zh., 53:6 (2012), 1413–1432; Siberian Math. J., 53:6 (2012), 1139–1154

Citation in format AMSBIB
\Bibitem{Sgi12} \by M.~S.~Sgibnev \paper Behavior at infinity of a~solution to a~differential-difference equation \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 6 \pages 1413--1432 \mathnet{http://mi.mathnet.ru/smj2393} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3074451} \elib{http://elibrary.ru/item.asp?id=18838189} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 6 \pages 1139--1154 \crossref{https://doi.org/10.1134/S0037446612060183} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312906500018} \elib{http://elibrary.ru/item.asp?id=20482482} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871678352} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. S. Sgibnev, “Behavior at infinity of a solution to a matrix differential-difference equation”, Siberian Math. J., 55:3 (2014), 530–543
2. M. S. Sgibnev, “Asymptotic expansion of the solution of a matrix differential-difference equation of the general form”, Differ. Equ., 52:1 (2016), 28–38
3. M. S. Sgibnev, “Exact asymptotics of the solution to a difference equation of general type”, J. Math. Sci., 231:2 (2018), 267–277
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