A sharp oscillation criterion for a linear delay differential equation

Ábel Garab, M. Pituk, Ioannis P. Stavroulakis

Research output: Contribution to journalArticle

Abstract

It is well-known that for the oscillation of all solutions of the linear delay differential equation x (t)+p(t)x(t−τ)=0,t≥t 0 , with p∈C([t 0 ,∞),R + ) and τ>0 it is necessary that B≔lim supt→∞A(t)≥[Formula presented],whereA(t)≔∫ t−τ t p(s)ds. Our main result shows that if the function A is slowly varying at infinity (in additive form), then under mild additional assumptions B>[Formula presented] implies the oscillation of all solutions of the above linear delay differential equation. The applicability of the obtained results and the importance of the slowly varying assumption on A are illustrated by examples.

Original languageEnglish
Pages (from-to)58-65
Number of pages8
JournalApplied Mathematics Letters
Volume93
DOIs
Publication statusPublished - Jul 1 2019

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Oscillation Criteria
Delay Differential Equations
Linear differential equation
Differential equations
Oscillation
Infinity
Imply
Necessary
Form

Keywords

  • Delay differential equation
  • Oscillation
  • S-asymptotically periodic function
  • Slowly varying function

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

A sharp oscillation criterion for a linear delay differential equation. / Garab, Ábel; Pituk, M.; Stavroulakis, Ioannis P.

In: Applied Mathematics Letters, Vol. 93, 01.07.2019, p. 58-65.

Research output: Contribution to journalArticle

Garab, Ábel ; Pituk, M. ; Stavroulakis, Ioannis P. / A sharp oscillation criterion for a linear delay differential equation. In: Applied Mathematics Letters. 2019 ; Vol. 93. pp. 58-65.
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