Approximation properties of solutions to multipoint boundary-value problems - Murach, A. A.; Pelekhata, O. B.; Soldatov, V. O.; Мурач, А. А.; Пелехатая, О. Б.; Солдатов, В. О.; Мурач, О. О.; Пелехата, О. Б.; Солдатов, В. О. (Institute of Mathematics, NAS of Ukraine, 2021)
UDC 517.927 We consider a wide class of linear boundary-value problems for systems of $m$ ordinary differential equations of order $r$ known as the general boundary-value problems. Their solutions $y\colon[a,b]→ \mathbb{C}^{m}$ belong to the Sobolev space $(W_1^{r})^m,$ and the boundary conditions are given in the form $By=q$ where $B\colon(C^{(r-1)})^{m}→\mathbb{C}^{rm}$ is an arbitrary continuous linear operator. For such a problem, we prove that its solution can be approximated in $(W_1^{r})^m$ with arbitrary precision by solutions to multipoint boundary-value problems with the same right-hand sides. These multipoint problems are built explicitly and do not depend on the right-hand sides of the general boundary-value problem. For these problems, we obtain estimates of error of solutions in the normed spaces $(W_1^{r})^m$ and $(C^{(r-1)})^{m}.$