On periodic solutions of systems of linear functional-differential equations

Ivan Kiguradze; Bedřich Půža

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 3, page 197-212
  • ISSN: 0044-8753

Abstract

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This paper deals with the system of functional-differential equations d x ( t ) d t = p ( x ) ( t ) + q ( t ) , where p : C ω ( R n ) → L ω ( R n ) is a linear bounded operator, q ∈ L ω ( R n ) , ω > 0 and C ω ( R n ) and L ω ( R n ) are spaces of n -dimensional ω -periodic vector functions with continuous and integrable on [ 0 , ω ] components, respectively. Conditions which guarantee the existence of a unique ω -periodic solution and continuous dependence of that solution on the right hand side of the system considered are established.

How to cite

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Kiguradze, Ivan, and Půža, Bedřich. "On periodic solutions of systems of linear functional-differential equations." Archivum Mathematicum 033.3 (1997): 197-212. <http://eudml.org/doc/18497>.

@article{Kiguradze1997,
abstract = {This paper deals with the system of functional-differential equations \[ \frac\{dx(t)\}\{dt\}=p(x)(t)+q(t), \] where $p:C_\omega (\{R\}^n)\rightarrow L_\omega (\{R\}^n)$ is a linear bounded operator, $q\in L_\omega (\{R\}^n)$, $\omega >0$ and $C_\omega (\{R\}^n)$ and $L_\omega (\{R\}^n)$ are spaces of $n$-dimensional $\omega $-periodic vector functions with continuous and integrable on $[0,\omega ]$ components, respectively. Conditions which guarantee the existence of a unique $\omega $-periodic solution and continuous dependence of that solution on the right hand side of the system considered are established.},
author = {Kiguradze, Ivan, Půža, Bedřich},
journal = {Archivum Mathematicum},
keywords = {linear functional-differential system; differential system with deviated argument; $\omega $-periodic solution; linear functional-differential equations; periodic solutions; uniqueness},
language = {eng},
number = {3},
pages = {197-212},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On periodic solutions of systems of linear functional-differential equations},
url = {http://eudml.org/doc/18497},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Kiguradze, Ivan
AU - Půža, Bedřich
TI - On periodic solutions of systems of linear functional-differential equations
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 3
SP - 197
EP - 212
AB - This paper deals with the system of functional-differential equations \[ \frac{dx(t)}{dt}=p(x)(t)+q(t), \] where $p:C_\omega ({R}^n)\rightarrow L_\omega ({R}^n)$ is a linear bounded operator, $q\in L_\omega ({R}^n)$, $\omega >0$ and $C_\omega ({R}^n)$ and $L_\omega ({R}^n)$ are spaces of $n$-dimensional $\omega $-periodic vector functions with continuous and integrable on $[0,\omega ]$ components, respectively. Conditions which guarantee the existence of a unique $\omega $-periodic solution and continuous dependence of that solution on the right hand side of the system considered are established.
LA - eng
KW - linear functional-differential system; differential system with deviated argument; $\omega $-periodic solution; linear functional-differential equations; periodic solutions; uniqueness
UR - http://eudml.org/doc/18497
ER -

References

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