Skip to main content
SpringerLink
Log in

Violation of unique solvability of the Dirichlet problem on the disk for systems of second-order differential equations

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We study the Dirichlet problem for the system of elliptic equations with matrix complex-valued coefficients

$$au_{x_1 x_1 }^ {\text{ + }}bu_{x_1 x_2 }^ {\text{ + }}cu_{x_1 x_1 }^ {\text{ = 0, }}x \in K,{\text{ }}u|\partial K{\text{ }} = 0$$

We are concerned with the case in which this homogeneous system of equations can have a countable number of linearly independent solutions.

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. A. V. Bitsadze, “On unique solvability of the Dirichlet problem for elliptic partial differential equations,”Uspekhi Mat. Nauk [Russian Math. Surveys],3, No. 6, 211–212 (1948).

    MATH  Google Scholar 

  2. A. V. Bitsadze,Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).

    MATH  Google Scholar 

  3. V. P. Burskii, “On the violation of unique solvability of the Dirichlet problem for elliptic systems on the disk,”Mat. Zametki [Math. Notes],48, No. 3, 32–36 (1990).

    Google Scholar 

  4. F. R. Gantmakher,The Theory of Matrices [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  5. M. Markus and Kh. Mink,Survey on the Theory of Matrices and Matrix Inequalities [in Russian], Nauka, Moscow (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk

    V. P. Burskii

Authors
  1. V. P. Burskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 23–27, January, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burskii, V.P. Violation of unique solvability of the Dirichlet problem on the disk for systems of second-order differential equations. Math Notes 65, 20–23 (1999). https://doi.org/10.1007/BF02675005

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02675005

Key Words

Search

Navigation