# On an antiperiodic type boundary value problem for first order linear functional differential equations

Robert Hakl; Alexander Lomtatidze; Jiří Šremr

Archivum Mathematicum (2002)

- Volume: 038, Issue: 2, page 149-160
- ISSN: 0044-8753

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topHakl, Robert, Lomtatidze, Alexander, and Šremr, Jiří. "On an antiperiodic type boundary value problem for first order linear functional differential equations." Archivum Mathematicum 038.2 (2002): 149-160. <http://eudml.org/doc/248952>.

@article{Hakl2002,

abstract = {Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem \[ u^\{\prime \}(t)=\ell (u)(t)+q(t),\qquad u(a)+\lambda u(b)=c \]
are established, where $\ell :C([a,b];R)\rightarrow L([a,b];R)$ is a linear bounded operator, $q\in L([a,b];R)$, $\lambda \in R_+$, and $c\in R$. The question on the dimension of the solution space of the homogeneous problem \[ u^\{\prime \}(t)=\ell (u)(t),\qquad u(a)+\lambda u(b)=0 \]
is discussed as well.},

author = {Hakl, Robert, Lomtatidze, Alexander, Šremr, Jiří},

journal = {Archivum Mathematicum},

keywords = {linear functional differential equation; antiperiodic type BVP; solvability and unique solvability; linear functional differential equation; antiperiodic type BVP; solvability and unique solvability},

language = {eng},

number = {2},

pages = {149-160},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On an antiperiodic type boundary value problem for first order linear functional differential equations},

url = {http://eudml.org/doc/248952},

volume = {038},

year = {2002},

}

TY - JOUR

AU - Hakl, Robert

AU - Lomtatidze, Alexander

AU - Šremr, Jiří

TI - On an antiperiodic type boundary value problem for first order linear functional differential equations

JO - Archivum Mathematicum

PY - 2002

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 038

IS - 2

SP - 149

EP - 160

AB - Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)+\lambda u(b)=c \]
are established, where $\ell :C([a,b];R)\rightarrow L([a,b];R)$ is a linear bounded operator, $q\in L([a,b];R)$, $\lambda \in R_+$, and $c\in R$. The question on the dimension of the solution space of the homogeneous problem \[ u^{\prime }(t)=\ell (u)(t),\qquad u(a)+\lambda u(b)=0 \]
is discussed as well.

LA - eng

KW - linear functional differential equation; antiperiodic type BVP; solvability and unique solvability; linear functional differential equation; antiperiodic type BVP; solvability and unique solvability

UR - http://eudml.org/doc/248952

ER -

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