Long-time behaviour of solutions of delayed-type linear differential equations

Diblík, Josef: Long-time behaviour of solutions of delayed-type linear differential equations. (2018)

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Abstract

This paper investigates the asymptotic behaviour of the solutions of the retarded-type linear differential functional equations with bounded delays x˙(t) = −L(t, xt) when t → ∞. The main results concern the existence of two significant positive and asymptotically different solutions x = ϕ (t), x = ϕ ∗∗(t) such that limt→∞ ϕ ∗∗(t)/ϕ (t) = 0. These solutions make it possible to describe the family of all solutions by means of an asymptotic formula. The investigation basis is formed by an auxiliary linear differential functional equation of retarded type y˙(t) = L (t, yt) such that L (t, yt) ≡ 0 for an arbitrary constant initial function yt . A commented survey of the previous results is given with illustrative examples.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 47
ISSN: 1417-3875
Page Range: pp. 1-23
DOI: https://doi.org/10.14232/ejqtde.2018.1.47
Uncontrolled Keywords: Differenciálegyenlet - késleltetett, Differenciálegyenlet - lineáris
Additional Information: Bibliogr.: p. 20-23. ; összefoglalás angol nyelven
Date Deposited: 2019. Jun. 03. 06:04
Last Modified: 2020. Jul. 29. 12:29
URI: http://acta.bibl.u-szeged.hu/id/eprint/58138

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