Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 142–145 | Cite as

On the Uniqueness of the Solution of the Dirichlet Boundary Value Problem for Quasiharmonic Functions in a Non-Unit Disk



In this article the uniqueness of the solution of Dirichlet boundary value problem for quasiharmonic functions in arbitrary disk T r + = {z: |z| < r}, where r ≠ 1, is established. Also the non-uniqueness of the solution of this problem in a unit disk is proven.

Keywords and phrases

differential equations quasiharmonic function Dirichlet boundary value problem non-unit disk uniqueness of solution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. M. Rasulov, The Method of the Conjugation of Analytic Functions and Some of its Applications (Smolensk Gos. Univ., Smolensk, 2013) [in Russian].Google Scholar
  2. 2.
    K. M. Rasulov, “About the solution of boundary value problem of Dirichlet in classes of quasiharmonic functions of arbitrary genus in a circle,” Izv. Smolensk. Univ. 1 (25), 402–409 (2014).Google Scholar
  3. 3.
    K.W. Bauer, “Uber eine der Differentialgleichung \({\left( {1 + z\bar z} \right)^2}{W_{z\bar z}} \pm n\left( {n + 1} \right)W = 0\) zugeordnete Funktionentheorie,” Bonner Math. Schrift. 23 (1965).Google Scholar
  4. 4.
    G. M. Goluzin, The Geometric Theory of Complex-Valued Functions (Nauka, Moscow, 1966) [in Russian].MATHGoogle Scholar
  5. 5.
    P. Davis, The Schwartz Function and its Applications (TheMath. Assoc. of America, Washington, 1974).Google Scholar
  6. 6.
    C. Mathurin, “Fonction caracteristique d’un contour algebrique simple. Applications a l’equations de l’elasticite plan,” Publ. Sci. Tech. Minist. Aire. Not. Tech. 105, 1–83 (1962).Google Scholar
  7. 7.
    I. I. Privalov, Boundary Properties of Analytic Functions (Gos. Izdat. Tekh.-Teor. Liter., Moscow, Leningrad, 1950) [in Russian].Google Scholar
  8. 8.
    E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (Krieger, UK, 1984).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Smolensk State UniversitySmolenskRussia

Personalised recommendations