# On periodic solutions of systems of linear functional-differential equations

Archivum Mathematicum (1997)

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

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topKiguradze, 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 -

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