## Abstract

We obtain new, explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays (x(t) − a(t)x(g(t)))^{0} + b(t)x(h(t)) = 0, where |a(t)| ≤ A_{0} < 1, 0 < b_{0} ≤ b(t) ≤ B_{0}, assuming that all parameters of the equation are measurable functions. To analyze the exponential stability, we apply the Bohl-Perron theorem and a reduction of a neutral equation to an equation with an infinite number of non-neutral delay terms. This method has never before been used for this neutral equation; its application allows omitting a usual restriction |a(t)| < 1/2 in known asymptotic stability tests and the consideration of variable delays.

Original language | English |
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Pages (from-to) | 387-403 |

Number of pages | 17 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 2019 |

## Keywords

- Bohl-perron theorem
- Explicit stability conditions
- Neutral equations in hale form
- Uniform exponential stability
- Variable delays

## ASJC Scopus subject areas

- General Mathematics