We consider a wide class of linear boundary-value problems for systems of r-th order ordinary differential equations whose solutions range over the normed complex space <$E(C sup (n) ) sup m> of <$En~symbol У~r> times continuously differentiable functions <$Ey~:~[a,~b]~symbol О~{ romam bold C} sup m>. The boundary conditions for these problems are of the most general form By = q, where B is an arbitrary continuous linear operator from <$E(C sup (n) ) sup m> to <$E{ roman bold C} sup rm>. We prove that the solutions to the considered problems can be approximated in <$E(C sup (n) ) sup m> by solutions to some multipoint boundary-value problems. The latter problems do not depend on the right-hand sides of the considered problem and are built explicitly.

• Солдатов Віталій Олександрович (фізико-математичні науки)

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