### 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 language | English |
---|---|

Pages (from-to) | 58-65 |

Number of pages | 8 |

Journal | Applied Mathematics Letters |

Volume | 93 |

DOIs | |

Publication status | Published - Jul 1 2019 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*Applied Mathematics Letters*,

*93*, 58-65. https://doi.org/10.1016/j.aml.2019.01.042