Skip to main content
SpringerLink
Log in

Some boundary-value problems for a class of fourth-order differential equations on a graph

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We study the problem of nondegeneracy of some boundary-value problems for a class of fourth-order differential equations on a geometric graph (topological net), present conditions for the existence of the Green function for boundary-value problems under consideration, and analyze its principal properties.

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. O. M. Penkin and Yu. V. Pokornyi, “Boundary-value problem on a graph,” Differents. Uravn., 24, No. 4, 701–703 (1988).

    MATH  MathSciNet  Google Scholar 

  2. Yu. V. Pokornyi and I. G. Karelina, “Green function of the Dirichlet problem on a graph,” Dokl. Akad. Nauk SSSR, 318, No. 3, 542–544.

  3. Yu. V. Pokornyi, O. M. Penkin, and E. N. Provorotova, “On a vector boundary-value problem,” in: Boundary-Value Problems, Perm Polytechnical Institute, Perm (1983), pp. 64–70.

    Google Scholar 

  4. S. Nicaise, “Estimée du spectre du laplacien sur un réseau topologique fini,” C. R. Sc. Paris, Ser. A, 303, No. 8, 343–346. (1986).

    MATH  MathSciNet  Google Scholar 

  5. B. S. Pavlov and L. D. Fadeev, “Model of free electrons and the scattering problem,” Teor. Mat. Fiz., 55, No. 2, 257–269 (1983).

    Google Scholar 

  6. F. P. Gantmakher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems [in Russian], Gostekhizdat, Moscow-Leningrad 1950.

    Google Scholar 

  7. Yu. V. Pokornyi and K. P. Lazarev, “Some oscillation theorems for multipoint problems,” Differents. Uravn., 23, No. 4, 658–670 (1987).

    MathSciNet  Google Scholar 

Download references

Authors
  1. R. Mustafokulov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mustafokulov, R. Some boundary-value problems for a class of fourth-order differential equations on a graph. Ukr Math J 48, 530–536 (1996). https://doi.org/10.1007/BF02390613

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02390613

Keywords

Search

Navigation