Skip to main content
Log in

Asymptotic integration of the Riccati equation by methods of power geometry

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The Riccati equation is considered. Both continuable and noncontinuable solutions of this equation are studied. Asymptotic representations of its solutions are obtained by power geometry methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Riccati, Acta Eruditirum, 502–504 (1723).

    Google Scholar 

  2. A. I. Egorov, Riccati Equations (Nauka, Moscow, 2001) [in Russian].

    MATH  Google Scholar 

  3. A. D. Bryuno, Russ. Math. Surveys 59 (3), 429–480 (2004).

    Article  Google Scholar 

  4. I. V. Goryuchkina, On the Convergence of a Generalized Power Series Being a Formal Solution of an Algebraic ODE in the General Case, Preprint No. 67 IPM im. M.V. Keldysha RAN (Inst. Appl. Math., Russian Academy of Sciences, Moscow, 2014).

    Google Scholar 

  5. R. R. Gontsov and I. V. Goryuchkina, Asympt. Anal. 93 (4), 311–325 (2015).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. S. Samovol.

Additional information

Original Russian Text © V.S. Samovol, 2017, published in Doklady Akademii Nauk, 2017, Vol. 495, No. 5, pp. 496–499.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samovol, V.S. Asymptotic integration of the Riccati equation by methods of power geometry. Dokl. Math. 96, 373–376 (2017). https://doi.org/10.1134/S106456241704024X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106456241704024X

Navigation