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

summary: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