Ukrainian Mathematical Journal

, Volume 56, Issue 9, pp 1429–1462 | Cite as

Truncation method for countable-point boundary-value problems in the space of bounded number sequences

  • A. M. Samoilenko
  • Yu. V. Teplins’kyi
  • V. A. Nedokis


We consider possible methods for the reduction of a countable-point nonlinear boundary-value problem with nonlinear boundary condition on a segment to a finite-dimensional multipoint problem constructed on the basis of the original problem by the truncation method. The results obtained are illustrated by examples.


Boundary Condition Original Problem Number Sequence Nonlinear Boundary Nonlinear Boundary Condition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. P. Persidskii, Infinite Systems of Differential Equations. Differential Equations in Nonlinear Spaces [in Russian], Nauka, Alma-Ata (1976).Google Scholar
  2. 2.
    A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993).Google Scholar
  3. 3.
    O. M. Martynyuk, Investigation of Solutions of Boundary-Value Problems for Countable Systems of Nonlinear Differential Equations [in Ukrainian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Kiev (1993).Google Scholar
  4. 4.
    Yu. V. Teplinskii and V. A. Nedokis, “Limit theorems in the theory of multipoint boundary-value problems, ” Ukr. Mat. Zh., 51, No.4, 519–531 (1999).Google Scholar
  5. 5.
    Yu. V. Teplins’kyi and V. A. Nedokis, “On countable-point boundary-value problems for countable systems of ordinary differential equations,” Nelin. Kolyvannya, No. 2, 252–266 (1999).Google Scholar
  6. 6.
    A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods in the Theory of Boundary-Value Problems for Ordinary Differential Equations [in Russian], Naukova Dumka, Kiev (1992).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • Yu. V. Teplins’kyi
    • 2
  • V. A. Nedokis
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv
  2. 2.Kam’yanets’-Podil’s’kyi UniversityKam’yanets’-Podil’s’kyi

Personalised recommendations