Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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"
}