Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[{{x}^{\prime }(t) ={A}(t){x}(\tau _{11}(t))+{B}(t){u}(\tau _{12}(t)) +{q}_1(t)\,, {u}^{\prime }(t) ={C}(t){x}(\tau _{21}(t))+{D}(t){u}(\tau _{22}(t)) +{q}_2(t)\,, \alpha _{11} {x}(0) + \alpha _{12} {u}(0) = {c}_0, \quad \alpha _{21} {x}(T) + \alpha _{22} {u}(T) = {c}_T} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.
@article{107825,
author = {Jan Kubal\v c\'\i k},
title = {On a two point linear boundary value problem for system of ODEs with deviating arguments},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {101-118},
zbl = {1087.34044},
mrnumber = {1909592},
language = {en},
url = {http://dml.mathdoc.fr/item/107825}
}
Kubalčík, Jan. On a two point linear boundary value problem for system of ODEs with deviating arguments. Archivum Mathematicum, Tome 038 (2002) pp. 101-118. http://gdmltest.u-ga.fr/item/107825/
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