Skip to main content
SpringerLink
Log in

On the uniqueness of solutions to some boundary-value problems for differential equations in a domain with algebraic boundary

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Classes of differential equations with constant coefficients admitting unique solutions of Dirichlet and Cauchy boundary-value problems are considered in a bounded domain with algebraic boundary. For the Dirichlet problem in a ball, the necessary and sufficient conditions for the uniqueness of the solution are obtained in the form of a countable sequence of inequalities polynomial in the coefficients of the equation.

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. B. I. Ptashnik,Incorrect Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  2. V. P. Burskii, “On the violation of the uniqueness of a solution to the Dirichlet problem for the elliptic systems on the disk,”Mat. Zametki,48, No. 3, 32–36 (1990).

    Google Scholar 

  3. V. P. Burskii, “Some boundary-value problems for the systems of differential equations of the first order with the homogeneous symbol on the disk,”Mat. Fiz. Nelin. Mekh., No. 9, 32–35 (1988).

    Google Scholar 

  4. V. P. Burskii, “On boundary-value problems for the equations of the third and fourth orders with constant coefficients on the disk,”Mat. Fiz. Nelin. Mekh., No. 4, 76–81 (1985).

    Google Scholar 

  5. V. P. Burskii, “The uniqueness of a solution to the Dirichlet problem in the ball for the wave equation,”Differents. Uravn.,24, No. 6, 1038–1039 (1988).

    Google Scholar 

  6. V. P. Burskii, “Remarks on the Dirichlet problem for the ultrahyperbolic equation in the ball and the integral geometry on the sphere,”Uspekhi Mat. Nauk,43, No. 5, 181–182 (1988).

    Google Scholar 

  7. V. P. Burskii, “Boundary-value problems for a hyperbolic equation of the second order on the disk,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 22–29 (1987).

    Google Scholar 

  8. V. P. Burskii, “Boundary properties of theL 2-solutions to linear differential equations and the equation-domain duality,”Dokl. Akad. Nauk SSSR,309, No. 5, 1036–1039 (1989).

    Google Scholar 

  9. M. Marcus and H. Minc,A Survey of Matrix Theory and Matrix Inequalities [Russian translation], Nauka, Moscow (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, 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 from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 898–906, July, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burskii, V.P. On the uniqueness of solutions to some boundary-value problems for differential equations in a domain with algebraic boundary. Ukr Math J 45, 993–1003 (1993). https://doi.org/10.1007/BF01057446

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057446

Keywords

Search

Navigation