Open Access

# Approximation properties of multipoint boundary-value problems

### 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.

### 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},
}

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