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

Abstract

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Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) + λ u ( b ) = c are established, where ℓ : C ( [ a , b ] ; R ) → L ( [ a , b ] ; R ) is a linear bounded operator, q ∈ L ( [ a , b ] ; R ) , λ ∈ R + , and c ∈ R . The question on the dimension of the solution space of the homogeneous problem u ' ( t ) = ℓ ( u ) ( t ) , u ( a ) + λ u ( b ) = 0 is discussed as well.

How to cite

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Hakl, 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 -

References

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