This article is cited in 4 papers

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.

UDC: 517.929.8

Received: 24.05.2011

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

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