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.
@article{107828,
author = {Robert Hakl and Alexander Lomtatidze and Ji\v r\'\i\ \v Sremr},
title = {On an antiperiodic type boundary value problem for first order linear functional differential equations},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {149-160},
zbl = {1087.34042},
mrnumber = {1909595},
language = {en},
url = {http://dml.mathdoc.fr/item/107828}
}
Hakl, Robert; Lomtatidze, Alexander; Šremr, Jiří. On an antiperiodic type boundary value problem for first order linear functional differential equations. Archivum Mathematicum, Tome 038 (2002) pp. 149-160. http://gdmltest.u-ga.fr/item/107828/
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