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.


Full Text





Article Information

TitleApproximation properties of multipoint boundary-value problems
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 2, 119-125
DOIhttps://doi.org/10.31392/MFAT-npu26 2.2020.04
MilestonesReceived 04.05.2020
CopyrightThe 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


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



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},
       URL = {http://mfat.imath.kiev.ua/article/?id=1344},
}


References

Coming Soon.

All Issues