Abstract
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 $(C^{(n)})^m$ of
$n\geq r$ times continuously differentiable functions
$y:[a,b]\to\mathbb{C}^{m}$. The boundary conditions for these
problems are of the most general form $By=q$, where $B$ is an
arbitrary continuous linear operator from $(C^{(n)})^{m}$ to
$\mathbb{C}^{rm}$. We prove that the solutions to the considered
problems can be approximated in $(C^{(n)})^m$ 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.
Key words: Differential system, boundary-value problem, multipoint problem, approximation of solution.
Full Text
Article Information
| Title | Approximation properties of multipoint boundary-value problems |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 2, 119-125 |
| DOI | 10.31392/MFAT-npu26_2.2020.04 |
| MathSciNet |
MR4127609 |
| Milestones | Received 04.05.2020 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
O. Pelekhata
National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Peremohy Avenue 37, 03056, Kyiv-56, Ukraine
H. Masliuk
National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Peremohy Avenue 37, 03056, Kyiv-56, Ukraine
V. Soldatov
National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Peremohy Avenue 37, 03056, Kyiv-56, Ukraine
Citation Example
H. Masliuk, O. Pelekhata, and V. Soldatov, Approximation properties of multipoint boundary-value problems, Methods Funct. Anal. Topology 26
(2020), no. 2, 119-125.
BibTex
@article {MFAT1344,
AUTHOR = {H. Masliuk and O. Pelekhata and V. Soldatov},
TITLE = {Approximation properties of multipoint boundary-value problems},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {2},
PAGES = {119-125},
ISSN = {1029-3531},
MRNUMBER = {MR4127609},
DOI = {10.31392/MFAT-npu26_2.2020.04},
URL = {http://mfat.imath.kiev.ua/article/?id=1344},
}
