Skip to main content
SpringerLink
Log in

Fredholm property of boundary value problems for a fourth-order elliptic differential-operator equation with operator boundary conditions

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

In a Hilbert space H, we study the Fredholm property of a boundary value problem for a fourth-order differential-operator equation of elliptic type with unbounded operators in the boundary conditions. We find sufficient conditions on the operators in the boundary conditions for the problem to be Fredholm. We give applications of the abstract results to boundary value problems for fourth-order elliptic partial differential equations in nonsmooth domains.

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. Yakubov, S. and Yakubov, Ya., Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall/CRC, Boca Raton, 2000.

    MATH  Google Scholar 

  2. Yakubov, S.Ya., Fredholm Property for Elliptic Boundary Value Problems of Partial Differential and Differential-Operator Equations, Results Math., 1993, vol. 24, pp. 372–388.

    Article  MATH  MathSciNet  Google Scholar 

  3. Favini, A. and Yakubov, Ya., Regular Boundary Value Problems for Elliptic Differential-Operator Equations of the Fourth Order in UMD Banach Spaces, Sci. Math. Jpn., 2009, vol. 70, no. 2, pp. 183–204.

    MATH  MathSciNet  Google Scholar 

  4. Aliev, B.A. and Yakubov, Ya., Second Order Elliptic Differential-Operator Equations with Unbounded Operator Boundary Conditions in UMD Banach Spaces, Integral Equations Operator Theory, 2011, vol. 69, pp. 269–300.

    Article  MATH  MathSciNet  Google Scholar 

  5. Aliev, B.A., A Boundary Value Problem for a Second Order Elliptic Differential-Operator Equation with a Spectral Parameter and Operator Boundary Conditions, Proc. IMM of NAS of Azerbaijan, 2010, vol. 32, pp. 21–46.

    MATH  Google Scholar 

  6. Krein, S.G., Lineinye differentsial’nye uravneniya v banakhovom prostranstve (Linear Differential Equations in a Banach Space), Moscow: Nauka, 1967.

    Google Scholar 

  7. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, Berlin: Birkhäuser, 1977. Translated under the title Teoriya interpolyatsii, funktsional’nye prostranstva, differentsial’nye operatory, Moscow: Mir, 1980.

    Google Scholar 

  8. Evzerov, I.D. and Sobolevskii, P.E., Fractional Powers of Ordinary Differential Operators, Differ. Uravn., 1973, vol. 9, no. 2, pp. 228–240.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan

    B. A. Aliev & Ya. Yakubov

Authors
  1. B. A. Aliev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya. Yakubov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. A. Aliev.

Additional information

Original Russian Text © B.A. Aliev, Ya.Yakubov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 2, pp. 210–216.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aliev, B.A., Yakubov, Y. Fredholm property of boundary value problems for a fourth-order elliptic differential-operator equation with operator boundary conditions. Diff Equat 50, 213–219 (2014). https://doi.org/10.1134/S0012266114020086

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266114020086

Keywords

Search

Navigation