Skip to main content
SpringerLink
Log in

Number of solutions of the Dirichlet problem for equations elliptic on a set of solutions

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Literature cited

  1. C. Foias and R. Temam, “Structure of the set of stationary solutions of the Navier -Stokes equations,” Commun. Pure Appl. Math.,30, 149–164 (1977).

    Google Scholar 

  2. J. C. Saut and R. Temam, “Generic properties of Navier-Stokes equations: genericity with respect to the boundary values,” Indiana Univ. Math. J.,29, No. 3, 427–446 (1980).

    Google Scholar 

  3. P. Quittner, “Generic properties of von Karman equations,” Comment. Math. Univ. Carol.,23, No. 2, 399–413 (1982).

    Google Scholar 

  4. A. J. Tromba, “On the number of simply connected minimal surfaces spanning a curve,” Am. Math. Soc. Memoirs,12, No. 194 (1977).

  5. J. C. Saut and R. Temam, “Generic properties of nonlinear boundary value problems,” Commun. Part. Diff. Equat.,4, No. 3, 293–319 (1979).

    Google Scholar 

  6. M. Schlechter, “Various types of boundary conditions for elliptic equations,” Commun. Pure Appl. Math.,13, No. 3, 407–425 (1960).

    Google Scholar 

  7. L. Hörmander, “On the uniqueness of the Cauchy problem. II,” Mat. Scand.,7, 177–190 (1969).

    Google Scholar 

  8. I. V. Skrypnik and A. E. Shishkov, “On solvability of the Dirichlet problem for the Monge-Ampere equations,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 216–219 (1978).

    Google Scholar 

  9. I. Ya. Bakel'man, Geometric Methods in the Solution of Elliptic Equations [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  10. Yu. G. Borisovich and V. G. Zvyagin, “On a topological principle for solvability of equations with Fredholm operators,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 204–207 (1978).

    Google Scholar 

  11. M. A. Krasnosel'skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voronezh State University, Voronezh

    V. G. Zvyagin

Authors
  1. V. G. Zvyagin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskii Zametki, Vol. 49, No. 4, pp. 47–54, April, 1991.

The author wishes to thank A. S. Mishchenko and Yu. P. Solov'ev for discussing this paper with me.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zvyagin, V.G. Number of solutions of the Dirichlet problem for equations elliptic on a set of solutions. Mathematical Notes of the Academy of Sciences of the USSR 49, 365–369 (1991). https://doi.org/10.1007/BF01158210

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158210

Keywords

Search

Navigation