On the asymptotics of solutions of a class of linear functional-differential equations

G. Derfel, F. Vogl

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

A sharp estimate of the growth of solutions of the initial value problem for systems of the form u̇(t) = ∑lj=1 Cj(t) u(λj t), t ≥ t0 > 0, 0 < λj < 1, u(t) = φ(t) for λt0 ≤ t ≤ t0, λ = min λj, where Cj(t) are matrices with elements of power growth, is found. As a corollary of this result, it follows, for instance, that each solution of the initial value problem satisfies the estimate ∥u(t)∥ ≤ C exp{γln2(1 + |t|)} for some C > 0 and γ > 0.

Original languageEnglish
Pages (from-to)511-518
Number of pages8
JournalEuropean Journal of Applied Mathematics
Volume7
Issue number5
DOIs
StatePublished - 1 Jan 1996

ASJC Scopus subject areas

  • Applied Mathematics

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