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.