Detail publikace

Existence of Strictly Decreasing Positive Solutions of Linear Differential Equations of Neutral Type

DIBLÍK, J. SVOBODA, Z.

Originální název

Existence of Strictly Decreasing Positive Solutions of Linear Differential Equations of Neutral Type

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

DIBLÍK, J.; SVOBODA, Z.

Vydáno

1. 1. 2020

Nakladatel

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

Místo

USA

ISSN

1937-1632

Periodikum

Discrete and Continuous Dynamical Systems - Series S

Ročník

13

Číslo

1

Stát

Spojené státy americké

Strany od

67

Strany do

84

Strany počet

18

URL

http://www.aimsciences.org/article/doi/10.3934/dcdss.2020004

BibTex

@article{BUT165845,
  author="Josef {Diblík} and Zdeněk {Svoboda}",
  title="Existence of Strictly Decreasing Positive Solutions of Linear Differential Equations of Neutral Type",
  journal="Discrete and Continuous Dynamical Systems - Series S",
  year="2020",
  volume="13",
  number="1",
  pages="67--84",
  doi="10.3934/dcdss.2020004",
  issn="1937-1632",
  url="http://www.aimsciences.org/article/doi/10.3934/dcdss.2020004"
}