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On a two point linear boundary value problem for system of ODEs with deviating
arguments

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*Jan Kubalcik*

**Address.** Department of Mathematical Analysis, Faculty of Science,
Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
**E-mail:** kubalis@math.muni.cz

**Abstract.** Two point boundary value problem for the linear system
of ordinary differential equations with deviating arguments $$\eqalign
{\bold{x}'(t) &=\bold{A}(t)\bold{x}(\tau_{11}(t))+\bold{B}(t)\bold{u}(\tau_{12}(t))
+\bold{q}_1(t)\,, \cr \bold{u}'(t) &=\bold{C}(t)\bold{x}(\tau_{21}(t))+\bold{D}(t)\bold{u}(\tau_{22}(t))
+\bold{q}_2(t)\,, \cr \alpha_{11} \bold{x}(0) &+ \alpha_{12} \bold{u}(0)
= \bold{c}_0, \quad \alpha_{21} \bold{x}(T) + \alpha_{22} \bold{u}(T) =
\bold{c}_T} $$ 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.

**AMSclassification.** 34B10, 34B05, 34K10

**Keywords.** Existence and uniqueness of solution, two point linear
boundary value problem, linear system of ordinary differential equations,
deviating argument, delay.