Detail publikačního výsledku

On the dimension of the solutions set to the homogeneous linear functional differential equation of the first order

PŮŽA, B.; HAKL, R.; DOMOSHNITSKY, A.

Original Title

On the dimension of the solutions set to the homogeneous linear functional differential equation of the first order

English Title

On the dimension of the solutions set to the homogeneous linear functional differential equation of the first order

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.

English abstract

Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.

Keywords

functional differential equation; boundary value problem; differential inequality; solution set

Key words in English

functional differential equation; boundary value problem; differential inequality; solution set

Authors

PŮŽA, B.; HAKL, R.; DOMOSHNITSKY, A.

RIV year

2013

Released

31.12.2012

Publisher

Institute of Mathematics ASCR

Location

Praha

ISBN

0011-4642

Periodical

CZECHOSLOVAK MATHEMATICAL JOURNAL

Volume

62

Number

4

State

Czech Republic

Pages from

1033

Pages to

1053

Pages count

20

Full text in the Digital Library

http://hdl.handle.net/

BibTex

@article{BUT97937,
  author="Bedřich {Půža} and Robert {Hakl} and Alexander {Domoshnitsky}",
  title="On the dimension of the solutions set to the homogeneous linear functional differential equation of the first order",
  journal="CZECHOSLOVAK MATHEMATICAL JOURNAL",
  year="2012",
  volume="62",
  number="4",
  pages="1033--1053",
  issn="0011-4642"
}