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A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems


Abstract

We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\geq1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\leq n\in\mathbb{Z}.$ The boundary conditions can contain derivatives of order $l$, with $r\leq l\leq n+r$, of the solutions. We obtain a constructive criterion under which the solutions to these problems are continuous with respect to the parameter in the normed space $C^{(n+r)}$. We also obtain a two-sided estimate for the degree of convergence of these solutions.

Key words: Differential system, boundary-value problem, continuity in parameter.


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Article Information

TitleA criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 375-386
MilestonesReceived 15/08/2016
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

Vladimir Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine; National Technical University of Ukraine ”Kyiv Polytechnic Institute”, 37 Prospect Peremogy, Kyiv, 03056, Ukraine

Aleksandr Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine; Chernihiv National Pedagogical University, 53 Het’mana Polubotka, Chernihiv, 14013, Ukraine

Vitalii Soldatov
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine


Citation Example

Vladimir Mikhailets, Aleksandr Murach, and Vitalii Soldatov, A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems, Methods Funct. Anal. Topology 22 (2016), no. 4, 375-386.


BibTex

@article {MFAT915,
    AUTHOR = {Mikhailets, Vladimir and Murach, Aleksandr and Soldatov, Vitalii},
     TITLE = {A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {375-386},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=915},
}


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