Skip to main content
SpringerLink
Log in

Solutions of one-dimensional boundary-value problems with a parameter in Sobolev spaces

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We consider the most general boundary-value problems for systems of m ordinary first-order differential equations. For the solutions of these problems, we find sufficient conditions for the continuity in parameter in the Sobolev space \( {{\left( {W_p^n} \right)}^m} \) with \( n\in \mathbb{N} \) and 1 ≤ p < ∞.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu. M. Berezansky, Z. G. Sheftel, and G. F. Us, Functional Analysis, Birkhäuser, Basel, 1996.

    Book  MATH  Google Scholar 

  2. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators, Amer. Math. Soc., Providence, RI, 1969.

    Google Scholar 

  3. T. I. Kodliuk and V. A. Mikhailets, “Continuity of the solutions of one-dimensional linear boundary-value problems in a parameter,” Dopov. NAN Ukr., No. 11, 7–14 (2010).

    Google Scholar 

  4. T. I. Kodliuk and V. A. Mikhailets, “Multipoint boundary-value problems with parameter in Sobolev spaces,” Dopov. NAN Ukr., No. 11, 15–19 (2012).

  5. T. I. Kodliuk and V. A. Mikhailets, “Limit theorems for one-dimensional boundary-value problems,” Ukr. Math. J., 65, No. 1, (2013).

  6. N. V. Reva, Continuity of Solutions of Linear Boundary-Value Problems in a Parameter [in Ukrainian], PhD Dissertation, Institute of Mathematics of the NAS of Ukraine, Kiev, 2009.

  7. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications [in Russian], Nauka, Moscow, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkovskaya Str., Kiev, 01601, Ukraine

    Tatiana I. Kodliuk & Vladimir A. Mikhailets

Authors
  1. Tatiana I. Kodliuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir A. Mikhailets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatiana I. Kodliuk.

Additional information

Translated from Russian by V. V. Kukhtin

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 9, No. 4, pp. 546–559, October–November, 2012.

The work is supported by grant 01/01.12 of the NAS of Ukraine (under the joint Ukrainian–Russian project of the NAS of Ukraine and Russian Foundation for Basic Research).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kodliuk, T.I., Mikhailets, V.A. Solutions of one-dimensional boundary-value problems with a parameter in Sobolev spaces. J Math Sci 190, 589–599 (2013). https://doi.org/10.1007/s10958-013-1272-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-013-1272-2

Keywords

Search

Navigation