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

journal article in Web of Science

Language

en

Original Abstract

The paper is concerned with a linear neutral differential equation \dot y(t) = −c(t)y(t − τ(t)) + d(t) \dot y(t − δ(t)) where c: [t_0, ∞) → (0, ∞), d: [t_0, ∞) → [0, ∞), t_0 ∈ R and τ, δ : [t_0, ∞) → (0, r], r ∈ R , r > 0 are continuous functions. A new criterion is given for the existence of positive strictly decreasing solutions. The proof is based on the Rybakowski variant of a topological Wazewski principle suitable for differential equations of the delayed type. Unlike in the previous investigations known this time the progress is achieved by using a special system of initial functions satisfying a so-called sewing condition. The result obtained is extended to more general equations. Comparisons with known results are given as well.

English abstract

The paper is concerned with a linear neutral differential equation \dot y(t) = −c(t)y(t − τ(t)) + d(t) \dot y(t − δ(t)) where c: [t_0, ∞) → (0, ∞), d: [t_0, ∞) → [0, ∞), t_0 ∈ R and τ, δ : [t_0, ∞) → (0, r], r ∈ R , r > 0 are continuous functions. A new criterion is given for the existence of positive strictly decreasing solutions. The proof is based on the Rybakowski variant of a topological Wazewski principle suitable for differential equations of the delayed type. Unlike in the previous investigations known this time the progress is achieved by using a special system of initial functions satisfying a so-called sewing condition. The result obtained is extended to more general equations. Comparisons with known results are given as well.

Keywords

Delay; positive solution; neutral equation; sewing condition; retract method.

Released

01.01.2020

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA

Location

USA

ISBN

1937-1632

Periodical

Discrete and Continuous Dynamical Systems - Series S

Year of study

13

Number

1

State

US

Pages from

67

Pages to

84

Pages count

18

URL

Documents

BibTex


@article{BUT165845,
  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 linear neutral differential equation \dot y(t) = −c(t)y(t − τ(t)) + d(t) \dot y(t − δ(t))
where c: [t_0, ∞) → (0, ∞), d: [t_0, ∞) → [0, ∞), t_0 ∈ R and τ, δ : [t_0, ∞) → (0, r], r ∈ R , r > 0 are continuous functions. A new criterion is given for the existence of positive strictly decreasing solutions. The proof is based on the Rybakowski variant of a topological Wazewski principle suitable for differential equations of the delayed type. Unlike in the previous investigations known this time the progress is achieved by using a special system of initial functions satisfying a so-called sewing condition. The result obtained is extended to more general equations. Comparisons with known results are given as well.",
  address="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  chapter="165845",
  doi="10.3934/dcdss.2020004",
  howpublished="print",
  institution="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  number="1",
  volume="13",
  year="2020",
  month="january",
  pages="67--84",
  publisher="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  type="journal article in Web of Science"
}