Publication detail

Existence of strictly decreasing positive solutions of linear differential equations of neutral type

DIBLÍK, J. SVOBODA, Z.

Original Title

Existence of strictly decreasing positive solutions of linear differential equations of neutral type

English Title

Existence of strictly decreasing positive solutions of linear differential equations of neutral type

Type

conference paper

Language

en

Original Abstract

The paper is concerned with a system of linear neutral differential equations y'(t) = −C(t)y(t − τ (t)) + D(t)y'(t − δ (t)) where C and D are 2 × 2 matrices with positive entries and τ, δ are continuous delays. A criterion is derived for the existence of positive strictly decreasing components of solutions for t → ∞. The proof applies a variant of the topological Wazewski principle, as developed by Rybakowski, suitable for differential equations of the delayed type. The criterion derived generalizes a similar criterion for scalar linear neutral differential equations. Solutions of the problem are taken to be continuously differentiable defined by initial functions satisfying the sewing condition.

English abstract

The paper is concerned with a system of linear neutral differential equations y'(t) = −C(t)y(t − τ (t)) + D(t)y'(t − δ (t)) where C and D are 2 × 2 matrices with positive entries and τ, δ are continuous delays. A criterion is derived for the existence of positive strictly decreasing components of solutions for t → ∞. The proof applies a variant of the topological Wazewski principle, as developed by Rybakowski, suitable for differential equations of the delayed type. The criterion derived generalizes a similar criterion for scalar linear neutral differential equations. Solutions of the problem are taken to be continuously differentiable defined by initial functions satisfying the sewing condition.

Keywords

Neutral equation; delay; positive components; topological principle.

Released

24.07.2019

Publisher

AIP

ISBN

9780735418547

Book

AIP Conference Proceedings 2116

Pages from

310005-1

Pages to

310005-4

Pages count

4

URL

Documents

BibTex


@inproceedings{BUT158630,
  author="Josef {Diblík} and Zdeněk {Svoboda}",
  title="Existence of strictly decreasing positive solutions of linear differential equations of neutral type",
  annote="The paper is concerned with a system of linear neutral differential equations y'(t) = −C(t)y(t − τ (t)) + D(t)y'(t − δ (t)) where C and D are 2 × 2 matrices with positive entries and τ, δ are continuous delays. A criterion is derived for the existence of positive strictly decreasing components of solutions for t → ∞. The proof applies a variant of the topological Wazewski principle, as developed by Rybakowski, suitable for differential
equations of the delayed type. The criterion derived generalizes a similar criterion for scalar linear neutral differential equations. Solutions of the problem are taken to be continuously differentiable defined by initial functions satisfying the sewing condition.",
  address="AIP",
  booktitle="AIP Conference Proceedings 2116",
  chapter="158630",
  doi="10.1063/1.5114312",
  howpublished="electronic, physical medium",
  institution="AIP",
  number="1",
  year="2019",
  month="july",
  pages="310005-1--310005-4",
  publisher="AIP",
  type="conference paper"
}