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Ukrainian Mathematical Journal

, Volume 70, Issue 3, pp 410–421 | Cite as

Criteria for the Existence of an Isolated Solution of a Nonlinear Boundary-Value Problem

  • D. S. Dzhumabaev
  • S. M. Temesheva
Article

A nonlinear two-point boundary-value problem for an ordinary differential equation is studied by the method of parametrization. We construct systems of nonlinear algebraic equations that enable us to find the initial approximation to the solution to the posed problem. In terms of the properties of constructed systems, we establish necessary and sufficient conditions for the existence of an isolated solution to the analyzed boundary-value problem.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • D. S. Dzhumabaev
    • 1
    • 2
  • S. M. Temesheva
    • 3
    • 4
  1. 1.Institute of Mathematics and Mathematical SimulationMinistry of Education and ScienceAlmatyKazakhstan
  2. 2.International University of Information TechnologiesAlmatyKazakhstan
  3. 3.Institute of Mathematics and Mathematical SimulationMinistry of Education and ScienceAlmatyKazakhstan
  4. 4.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

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