Skip to main content
SpringerLink
Log in

Dirichlet Problem for a Mixed Type Equation of the Second Kind in Exceptional Cases

  • Short Communications
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We prove that the Dirichlet problem for a mixed-type equation of the second kind with an integer negative coefficient has a solution in a rectangular domain. The corresponding estimates are constructed and used to determine sufficient conditions for the problem to have a solution. The cases of nonuniqueness of the solution are distinguished, and solvability conditions in these cases are obtained.

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

References

  1. Khairullin, R.S., To the Dirichlet problem for a mixed-type equation of the second kind with strong degeneration, Differ. Equations, 2013, vol. 49, no. 4, pp. 510–516.

    Article  MathSciNet  MATH  Google Scholar 

  2. Khairullin, R.S., Solvability of the Dirichlet problem for a mixed-type equation of the second kind, Differ. Equations, 2017, vol. 53, no. 5, pp. 677–685.

    Article  MathSciNet  MATH  Google Scholar 

  3. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Abramowitz,M. and Stegun, I., Eds., Washington, D.C.: National Bureau of Standards, 1964. Translated under the title Spravochnik po spetsial’nym funktsiyam, Moscow: Nauka, 1979.

  4. Sabitov, K.B., Dirichlet problem for mixed-type equations in a rectangular domain, Dokl. Math., 2007, vol. 75, no. 2, pp. 193–196.

    Article  MathSciNet  MATH  Google Scholar 

  5. Sabitov, K.B. and Suleimanova, A.Kh., The Dirichlet problem for a mixed-type equation with characteristic degeneration in a rectangular domain, Russian Math., 2009, vol. 53, no. 11, pp. 37–65.

    Article  MathSciNet  MATH  Google Scholar 

  6. Safina, R.M., Keldysh problem for a mixed-type equation of the second kind with the Bessel operator, Differ. Equations, 2015, vol. 51, no. 10, pp. 1347–1359.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, Kazan, 420043, Russia

    R. S. Khairullin

Authors
  1. R. S. Khairullin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. S. Khairullin.

Additional information

Original Russian Text © R.S. Khairullin, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 4, pp. 565–568.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khairullin, R.S. Dirichlet Problem for a Mixed Type Equation of the Second Kind in Exceptional Cases. Diff Equat 54, 562–565 (2018). https://doi.org/10.1134/S0012266118040134

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266118040134

Search

Navigation