Publication result detail

Existence of solutions in cones to delayed higher-order differential equations

DIBLÍK, J.; GALEWSKI, M.

Original Title

Existence of solutions in cones to delayed higher-order differential equations

English Title

Existence of solutions in cones to delayed higher-order differential equations

Type

WoS Article

Original Abstract

An n-th order delayed differential equation y^{(n)}(t) = f(t, y_t, y′_t, . . . , y^{(n−1)}_t) is considered, where y_t(θ) = y(t + θ), θ ∈ [−τ, 0], τ > 0, if t → ∞. A criterion is formulated guaranteeing the existence of a solution y = y(t) in a cone 0 < (−1)^{i−1}y^{(i−1)}(t) < (−1)^{i−1}φ^{(i−1)}(t), i = 1, . . . , n where φ is an n-times continuously diff erentiable function such that 0 < (−1)^iφ^{(i)}(t), i = 0, . . . , n. The proof is based on a similar result proved first for a system of delayed differential equations equivalent in a sense. Particular linear cases are considered and an open problem is formulated as well.

English abstract

An n-th order delayed differential equation y^{(n)}(t) = f(t, y_t, y′_t, . . . , y^{(n−1)}_t) is considered, where y_t(θ) = y(t + θ), θ ∈ [−τ, 0], τ > 0, if t → ∞. A criterion is formulated guaranteeing the existence of a solution y = y(t) in a cone 0 < (−1)^{i−1}y^{(i−1)}(t) < (−1)^{i−1}φ^{(i−1)}(t), i = 1, . . . , n where φ is an n-times continuously diff erentiable function such that 0 < (−1)^iφ^{(i)}(t), i = 0, . . . , n. The proof is based on a similar result proved first for a system of delayed differential equations equivalent in a sense. Particular linear cases are considered and an open problem is formulated as well.

Keywords

Solution in a cone; Higher-order equation; Delayed diff erential equation; Long-time behaviour

Key words in English

Solution in a cone; Higher-order equation; Delayed diff erential equation; Long-time behaviour

Authors

DIBLÍK, J.; GALEWSKI, M.

RIV year

2022

Released

01.08.2022

Publisher

Elsevier

Location

Amsterdam

ISBN

0893-9659

Periodical

Applied Mathematics Letters

Volume

130

Number

108014

State

United States of America

Pages from

1

Pages to

7

Pages count

7

URL

https://www.sciencedirect.com/science/article/pii/S0893965921001221

BibTex

@article{BUT177095,
  author="Josef {Diblík} and Marek {Galewski}",
  title="Existence of solutions in cones to delayed higher-order differential equations",
  journal="Applied Mathematics Letters",
  year="2022",
  volume="130",
  number="108014",
  pages="1--7",
  doi="10.1016/j.aml.2022.108014",
  issn="0893-9659",
  url="https://www.sciencedirect.com/science/article/pii/S0893965921001221"
}